Publications

Books

  1. Computational Number Theory, M.E. Pohsttal, H.C. Williamssal \'es H.G. Zimmerrel, W. de Gruyter Publ. Co., 1991. {\bf MR} 92i:11131; {\bf Zbl} 722.00004
  2. Informatika a Fels\H{o}oktat\'asban, Herdon Mikl\'ossal, 1993.
  3. Number Theory: Diophantine, Computational and Algebraic Aspects,Proceedings, with K. Gy\H{o}ry and V.T. S\'os, W. de Gruyter Publ. Co., 1998.
  4. A. Pethõ, Algebraische Algorithmen, Vieweg Verlag, 1999.
  5. Informatika a Fels\H{o}oktat\'asban, Herdon Mikl\'ossal, 2005.
  6. Informatika a Fels\H{o}oktat\'asban, Herdon Mikl\'ossal, 2008.

Papers

  1. A. Pethõ, \"Uber die Darstellung rationalen Zahlen durch zerlegbare Formen, Publ. Math. Debrecen, {\bf 21} (1974), 31-38. {\bf MR} 50 \#7032; {\bf Zbl} 294.10013
  2. K. Gyõry et A. Pethõ, Sur la distribution des solutions des \'equations du type ''norm-forme", Acta Math. Acad. Sci. Hung., {\bf 26} (1975), 135-142. {\bf MR} 51 \#3052; {\bf Zbl} 302.10022
  3. K. Gyõry und A. Pethõ, \"Uber die Verteilung der L\"osungen von Normformen Gleichungen II., Acta Arith. {\bf 32} (1977), 349-363. {\bf MR} 55 \#2745; {\bf Zbl} 314.12015
  4. K. Gyõry und A. Pethõ, \"Uber die Verteilung der L\"osungen von Normformen Gleichungen III., Acta Arith., {\bf 37} (1980), 143-165. {\bf MR} 82e:10031; {\bf Zbl} 397.10010
  5. A. Pethõ, Diophantische Approximationen mit nat\"urlichen Zahlen, Publ. Math. Debrecen, {\bf 27} (1980), 131-137. {\bf MR} 81m:10065; {\bf Zbl} 453.10034
  6. A. Pethõ, \"Uber die nichtlineare Diophantische Approximation von quadratischen, algebraischen Zahlen, J.Number Theory {\bf 12} (1980), 334-338. {\bf MR} 81k:10052; {\bf Zbl} 433.10023
  7. Pethõ, Beitr\"age zur Theorie der S-Ordnungen, Acta Math. Acad. Sci. Hung., {\bf 37} (1981), 51-57. {\bf MR} 84e:12017; {\bf Zbl} 497.12003
  8. A. Pethõ, \"Uber die Verteilung der L\"osungen von S-Normformen Gleichungen, Publ. Math. Debrecen, {\bf 29} (1982), 1-17. {\bf MR} 85i:11025; {\bf Zbl} 502.10006
  9. Pethõ, Simple Continued Fractions for the Fredholm Numbers, J. Number Theory, {\bf 14} (1982), 232-236. {\bf MR} 83k:10015; {\bf Zbl} 481.10006
  10. A. Pethõ, Perfect Powers in Second Order Linear Recurrences, J. Number Theory, {\bf 15} (1982), 5-13. {\bf MR} 84f:10024; {\bf Zbl} 488.10009
  11. A. Pethõ and Gy. Reményi, On a Method for Establishing the Minimum Distance of Abelian Codes, Problems of Control and Inform. Theory, {\bf 11} (1982), 97- 105. {\bf MR} 84b:94023; {\bf Zbl} 495.94007
  12. Lakatos P. és Pethõ A., \'Abel f\'ele k\'odok egy oszt\'aly\'anak a vizsg\'alata sz\'am\'{\i}t\'og\'ep felhaszn\'al\'as\'aval, MTA SZTAKI K\"ozlem\'enyek, {\bf 25} (1982), 73-91.
  13. Buzási K., Lakatos P. és Pethõ A., Csoportk\'odok egy oszt\'aly\'anak k\'odt\'avols\'ag\'ar\'ol, Problem\"u Peredacsi Informacii, {\bf 17} (1982), 3-12. {\bf MR} 83j:94020; {\bf Zbl} 488.94023
  14. A. Pethõ, Full Cubes in the Fibonacci Sequences, Publ. Math. Debrecen, {\bf 30} (1983), 117-127. {\bf MR} 85j:11027; {\bf Zbl} 549.10007
  15. A. Pethõ, Perfect Powers in Second Order Recurrences, in {\em Topics in Classical Number Theory}, Budapest, 1981, 1217-1227. {\bf MR} 86i:11099; {\bf Zbl} 549.10008
  16. B. Kovács and A. Pethõ, Canonical Systems in the Ring of Integers, Publ. Math. Debrecen, {\bf 30} (1983), 39-45. {\bf MR} 86d:11014; {\bf Zbl} 539.10010
  17. I. Nemes and A. Pethõ, Polynomial Values in Linear Recurrences I., Publ. Math. Debrecen, {\bf 31} (1984), 229-233. {\bf MR} 86g:11010; {\bf Zbl} 557.10010
  18. I. Nemes and A. Pethõ, Polynomial Values in Linear Recurrences II., J. Number Theory, {\bf 24} (1986), 47-53. {\bf MR} 87i:11025; {\bf Zbl} 591.10007
  19. A. Pethõ, On the Solution of the Equation $G_n = P(x)$, in {\em Fibonacci Numbers and Their Applications}, D. Reidel Publ. Comp. 1986, 193-201. {\bf MR} 87m:11032; {\bf Zbl} 598.10030
  20. A. Pethõ, On the Diophantine Equation $G_n = p^z$ , in {\em Proceedings EUROCAL '85}, Lecture Notes in Comput. Sci.,Vol. 204. Springer Verlag, 1986, 503-512. {\bf MR} 87f:11021; {\bf Zbl} 578.10012
  21. J. Buchmann and A. Pethõ, Computation of Independent Units in Number Fields by Dirichlet's Method, (Extended abstract) in: {\em Algebraic Algorithms and Error-Correcting Codes}, Lecture Notes in Comput. Sci., Vol. 229. Springer Verlag, 1986, 302-305. {\bf MR} 87m:94005; {\bf Zbl} 597.12009
  22. A. Pethõ and B.M.M. de Weger, Product of Prime Powers in Binary Recurrence Sequences I., Math. Comp. {\bf 47} (1986), 713 -727. {\bf MR} 87m:11027a; {\bf Zbl} 623.10011
  23. G. Fazekas és Pethõ A., Permut\'aci\'os forr\'ask\'odol\'as, Alkalmazott Matematikai Lapok, {\bf 12} (1986), 107-110. {\bf MR} 88c:94015;
  24. A. Pethõ, On the Resolution of Thue Inequalities, J. Symbolic Computation, {\bf 4} (1987), 103-109. {\bf MR} 89b:11030; {\bf Zbl} 625.10025
  25. P. Bundschuh und A. Pethõ, Zur Transzendenz gewisser Reihen, Monatshefte der Math. {\bf 104} (1987), 199-223. {\bf MR} 89h:11036; {\bf Zbl} 601.10025
  26. {\sc A. Peth\H{o}} und {\sc R. Schulenberg} {\em Effektives L\"osen von Thue Gleichungen,} Publ. Math. Debrecen, {\bf 34} (1987) 189-196. {\bf MR} 89c:11044
  27. A. Pethõ, Divisibility properties of linear recursive sequences, in: {\em Number Theory}, Eds.: K. Gy\H{o}ry and G. Hal\'asz, Coll. Math. Soc. J\'anos Bolyai Vol.51. 1990, 899-915. {\bf MR} 91i:11019; {\bf Zbl} 705.11005
  28. A. Pethõ, Complexity investigations on decomposable form equations, Publ. Math. Deb\-recen, {\bf 39} (1991), 163-169. {\bf MR} 92j:11028; {\bf Zbl} 749.11058
  29. J. Buchmann and A. Pethõ, Computation of Independent Units in Number Fields by Dirichlet 's Method, Math. Comp. {\bf 52} (1989), 149-159 \'es S1-S14. {\bf MR} 90e:11162; {\bf Zbl} 665.12008
  30. A. Pethõ, On the representation of 1 by binary cubic forms with positive discriminant, {\em Number Theory}, Ulm 1987 Proceedings. H.P. Schlickewei and E.Wirsing Eds. Lecture Notes Math. Vol. 1380, Springer Verlag 1989. 185-196. {\bf Zbl} 677.10012
  31. A. Pethõ, Computational methods for the resolution of diophantine equations, {\em Number Theory}, Proc. First Conference of the Canadian Number Theory Association, 1988. R. Mollin Editor, Walter de Gruyter Publ. Comp., 1990, 479-492. {\bf MR} 92c:11152; {\bf Zbl} 704.11006
  32. A. Pethõ, On the greatest prime factor and divisibility properties of linear recursive sequences, Indag. Mathem. N.S. {\bf 1} (1990) 85-93. {\bf MR} 91e:11085; {\bf Zbl} 704.11008
  33. A. Pethõ and R.F. Tichy, On digit expansions with respect to linear recurrences, J. Number Theory {\bf 33} (1989), 243-256. {\bf MR} 91c:11008; {\bf Zbl} 676.1001
  34. {\sc B. Kov\'acs} and {\sc A. Peth\H{o}}, {\em On a representation of algebraic integers,} Studia Sci. Math. Hungar. {\bf 27} (1993), 169--172. {\bf MR} 94d:11080; {\bf Zbl} 805.11076.
  35. {\sc B. Kov\'acs} and {\sc A. Peth\H{o}}, {\em Number systems in integral domains especially in orders of algebraic number fields,} Acta Sci. Math. Szeged, {\bf 55} (1991) 287--299. {\bf MR} 92m:11116; {\bf Zbl} 760.11002.
  36. I. Gaál A. Pethõ und M. Pohst, On the resolution of index form equations in biquadratic number fields I. J. Number Theory, {\bf 38} (1991), 18-34. {\bf MR} 92g:11031; {\bf Zbl} 726.11022
  37. I. Gaál, A. Pethõ und M. Pohst, On the resolution of index form equations in biquadratic number fields II. J. Number Theory, {\bf 38} (1991), 35-51. {\bf MR} 92g:11031; {\bf Zbl} 726.11023
  38. J.P. Bézivin, A. Pethõ and A.J. van der Poorten, A full characterization of divisibility sequences Amer. J. Math., {\bf 112} (1990), 985-1001.). {\bf MR} 91k:11017; {\bf Zbl} 716.11008
  39. A. Pethõ and H.G. Zimmer, Lineare rekurrente Folgen auf elliptische Kurven, S\'em. Th\'eorie Nombr. Bordeaux {\bf 2} (1990), 217-227. {\bf MR} 91k:11044; {\bf Zbl} 712.11012
  40. A. Pethõ, On a polynomial transformation and its application to the construction of a public key cryptosystem, {\em Computational Number Theory}, Proc., Walter de Gruyter Publ. Comp. Eds.: A. Peth\H{o}, M. Pohst, H.G. Zimmer and H.C. Williams, 1991, pp 31-44. {\bf MR} 93e:94011e; {\bf Zbl} 733.94014
  41. A. Pethõ, Complete solutions to a family of quartic diophantine equations, Math. Comp. {\bf 57} (1991), 777-798. {\bf MR} 92e:11023; {\bf Zbl} 738.11028
  42. {\sc I. Ga\'al, A. Peth\H{o}} and {\sc M. Pohst}, {\em On the indices of biquadratic number fields with Galois group $V_4$,} Arch. Math. {\bf 57} (1991), 357-361. {\bf MR} 92h:11092; {\bf Zbl} 724.11049
  43. {\sc I. Ga\'al, A. Peth\H{o}} and {\sc M. Pohst}, {\em On the resolution of index form equations in biquadratic number fields III. The bicyclic biquadratic case,} J. Number Theory, {\bf 53} (1995), 100-114. {\bf Zbl} 853.11026
  44. {\sc A. Peth\H{o}}, {\em The Pell sequence contains only trivial perfect powers,} Proc. Sets Graphs and Numbers. Coll. Math. Soc. János Bolyai Vol. 60. pp 561--568. {\bf MR} 94e:11031; {\bf Zbl} 790.11021 Download
  45. {\sc A. Peth\H{o}}, {\em Application of Gr\"obner bases to the resolution of systems of norm equations,} {\em Proc. ISSAC '91}, Ed.: S.M. Watt, ACM Press 1991, pp. 144-150. Download
  46. {\sc I. Ga\'al, A. Peth\H{o}} and {\sc M. Pohst}, {\em On the resolution of index form equations,} {\em Proc. ISSAC '91}, Ed.: S.M. Watt, ACM Press 1991, pp. 185-186.
  47. {\sc K. Gy\H{o}ry} and {\sc A. Peth\H{o}}, {\em On second order linear divisibility sequences over algebraic number fields,} Publ. Math. Debrecen {\bf 39} (1991), 171-179.{\bf MR} 93i:11011; {\bf Zbl} 749.11015
  48. {\sc M. Mignotte, A. Peth\H{o}} and {\sc R. Roth}, {\em Complete solutions of quartic Thue and index form equations,} Math. Comp. {\bf 65} (1996), 341--354. {\bf MR} 96d:11034; {\bf Zbl} 853.11022 Download
  49. {\sc A. Peth\H{o}}, {\em \"Uber kubische Ausnahmeeinheiten,} Arch. Math. {\bf 60} (1993), 146--153. {\bf MR} 94d:11017; {\bf Zbl} 791.11056 Download
  50. {\sc A. Peth\H{o}}, {\em Systems of norm equations over cubic number fields,} Grazer Math. Ber. {\bf 318} (1992), 111--120. {\bf MR} 94f:11019; {\bf Zbl} 804.11027.
  51. {\sc A. Peth\H{o}} and {\sc R.F. Tichy} {\em S--Unit equations, linear recurrences and digit expansions,} Publ. Math. Debrecen, {\bf 42} (1993), 145--154. {\bf MR} 94a:11013; {\bf Zbl} 792.11006.
  52. {\sc M. Mignotte} et {\sc A. Peth\H{o},} {\em Sur les carr\'es dans certaines suites de Lucas,} Journal de Th\'eorie Nombres de Bordeaux, {\bf 5} (1993), 333-341 ; {\bf MR} 95a:11013; {\bf Zbl} 795.11007. Download
  53. {\sc M. Mignotte} et {\sc A. Peth\H{o},} {\em Az $a^n+b^n=z^3$ diofantoszi egyenletr\H{o}l,} Acta Acad. Paed. Agriensis, Sect. Math. (1995-96), 45--53. {\bf Zbl} 0881.11040 Download
  54. {\sc I. Ga\'al, A. Peth\H{o}} and {\sc M. Pohst}, {\em On the resolution of index form equations in quartic number fields,} J. Symbolic Computation {\bf 11} (1994) 1--22. ; {\bf MR} 95f:11109; {\bf Zbl} 808.11023.
  55. {\sc I. Ga\'al, A. Peth\H{o}} and {\sc M. Pohst}, {\em On the Resolution of Index Form Equations in Dihedral Quartic Number Fields,} Experimental Math. {\bf 3} (1994) 245--254. ; {\bf MR} 96a:11114; {\bf Zbl} 823.11074. Download
  56. {\sc I. Ga\'al, A. Peth\H{o}} and {\sc M. Pohst}, {\em Simultaneous representation of numbers by a pair of ternary quadratic forms -- with an application to index form equations in quartic fields,} J. Number Theory, {\bf 57} (1996), 90--104. {\bf Zbl} 853.11023 Download
  57. {\sc P.J. Grabner, I. Nemes , A. Peth\H{o}} and {\sc R.F. Tichy,} {\em Generalized Zeckendorf Expansions,} Applied Math. Letters Vol. 7, No. 2, (1994) 25-28, ; {\bf MR} 95f:11013ab; {\bf Zbl} 792.11002.
  58. {\sc P.J. Grabner, A. Peth\H{o}, R.F. Tichy }, and {\sc G.J. Woeginger,} {\em Associativity of Recurrence Multiplication,} Applied Math. Letters Vol. 7, No. 4, (1994) 85-90, ; {\bf MR} 96d:11019; {\bf Zbl} 815.11011.
  59. {\sc M. Mignotte} and {\sc A. Peth\H{o},} {\em On the system of diophantine equations $x^2-6y^2=-5$ and $x=2z^2-1$,} Math. Scandinavica, {\bf 76} (1995), 50--60. {\bf MR} 96d:11033; {\bf Zbl} 849.11031 Download
  60. {\sc J. Gebel , A. Peth\H{o}} and {\sc H.G. Zimmer,}{\em Computing integral points on elliptic curves,} Acta Arith. {\bf 68} (1994), 171--192. ; {\bf MR} 95i:11020; {\bf Zbl} 816.11019. Download
  61. {\sc G. Lettl} and {\sc A. Peth\H{o},}{\em Complete solution of a family of quartic Thue equations,} Hamburger Abhandlungen {\bf 65} (1995), 365--383. {\bf MR} 96h:11019; {\bf Zbl} 853.11021
  62. {\sc A. Peth\H{o}, Th. Weiss} and {\sc H.G. Zimmer,}{\em Torsion groups of elliptic curves with integral j-invariant over general cubic number fields,} Intern. J. Alg. Comp. {\bf 7} (1997), 353--413. {\bf Zbl} 868.11030
  63. {\sc I. Gy\H{o}ri, J. Karsai, A. Peth\H{o}} and {\sc A. Sali}, {\em Developments of computational methods and networking in medical institutions in Hungary}, in: "Building a Man in the Machine Computational Medicine, Public Health, and Biotechnology" Part III, ed.: M. Witten, Word Scientific Publ. Co. Pte. Ltd. (1995), pp. 1545--1562. Download
  64. {\sc F. Lemmermeyer} and {\sc A. Peth\H{o}}, {\em Simplest Cubic Fields}, Manuscripta math. {\bf 88} (1995), 53--58. {\bf MR} 96g:11128; {\bf Zbl} 851.11059
  65. {\sc T. Herendi } and {\sc A. Peth\H{o}}, {\em Trinomials, which are divisible by quadratic polynomials,} Acta Acad. Paed. Agriensis, Sect. Math. {\bf 22} (1994), 61--73.
  66. {\sc P.J. Grabner, I. Nemes, A. Peth\H{o}} and {\sc R.F. Tichy}, On the least significant digit of Zeckendorf expansions, Fibonacci Quart. {\bf 34} (1996), 147--151. {\bf Zbl} 851.11005
  67. {\sc J. Gebel, A. Peth\H{o}} and {\sc H.G. Zimmer}, On Mordell's equation, Compositio Math., {\bf 110} (1998), 335--367. Download  List of the solutions of Mordell's equation for $|k| \le 10,000$.
  68. {\sc M. Mignotte}, {\sc A. Peth\H{o}} and {\sc F. Lemmermeyer}, {\em On the family of Thue equations $x^3-(n-1)x^2y-(n+2)xy^2-y^3 = k$}, Acta Arith., {\bf 76} (1996), 245--269.{\bf Zbl} 862.11028 Download
  69. {\sc A. Peth\H{o}}, {\em On the periodic expansion of algebraic numbers}, Ann. Univ. Sci. Budapest E\"otv\"os, Sect. Comp., 18 (1999), 167--174. Download
  70. {\sc A. Peth\H{o}, J. Stein, Th. Weis} and {\sc H.G. Zimmer}, {\em Computing the torsion group of elliptic curves by the method of Groebner bases}, In: "Progress in Computer Science and Applied Logic," Vol.15, Ed.: V. Weisspfenning, Birkh\"auser Verlag, Basel, 1998, pp. 245--265.
  71. {\sc J. Gebel, A. Peth\H o} and {\sc H.G. Zimmer,} {\em Computing integral points on Mordell's elliptic curves.} Collectanea Mathematica, Band 48, Fasc. 1-2, 1997, 115-136. {\bf Zbl:} 865.11084
  72. {\sc J. Gebel, A. Peth\H o} and {\sc H.G. Zimmer,} {\em Computing $S$-integral points on elliptic curves.} In: "Algorithmic Number Theory", Ed.: H. Cohen. ANTS-II, Proceedings, Bordeaux 1996, Lect. Notes in Comp. Sci., {\bf 1122} (1996), 157--171. Springer-Verlag. Download
  73. {\sc F. Halter-Koch, G. Lettl, A. Peth\H o} and {\sc R.F. Tichy,} {\em Thue Equations associated with Ankeny-Brauer-Chowla Number Fields}, J. London Math. Soc. (2) {\bf 60} (1999), 1--20. Download
  74. {\sc G. Lettl, A. Peth\H o} and {\sc P. Voutier} {\em Simple families of Thue inequalities,} Trans. Amer. Math. Soc., 351(1999), 1871-1894.
  75. {\sc A. Peth\H{o}}, {\em Diophantine properties of linear recurrence sequences I.} In: "Applications of Fibonacci Numbers, Volume 7", Ed.: G.E. Bergum, Kluwer Academic Publishers, 1998, pp. 295--309.Download the document
  76. {\sc A. Peth\H o} and {\sc R.F. Tichy,} {\em On two parametric families of diophantine problems} J. Symbolic Computation, {\bf 26} (1998), 151--171.
  77. {\sc G. Lettl, A. Peth\H o} and {\sc P. Voutier} {\em On the arithmetic of simplest sextic fields and related Thue equations,} In: "Number Theory", Eds.: K. Gy\H{o}ry, A.Peth\H{o} and V.T. S\'os, Walter de Gruyter GmbH \& Co., Berlin-New York, 1998, pp. 331--348.
  78. {\sc A. Dujella} and {\sc A. Peth\H o,} {\em Generalization of a theorem of Baker and Davenport}, Quart. J. Math. Oxford (2), 49 (1998), 291--306. Download
  79. {\sc P. Kirschenhofer, A. Peth\H o} and {\sc R.F. Tichy,} {\em On analytical and diophantine properties of a family of counting functions}, Acta Sci. Math. 65 (1999), 47--59.
  80. {\sc A. Peth\H o, H.G. Zimmer, J. Gebel} and {\sc E. Herrmann,} {\em Computing all $S$-integral points on elliptic curves}, Math. Proc. Camb. Philos. Soc., 127 (1999), 383--402. Download
  81. {\sc A. Peth\H o, E. Herrmann} and {\sc H.G. Zimmer,} {\em $S$-integral points on elliptic curves and Fermat's triple equations,} in Algorithmic Number Theory, Ed.: J.P. Buhler, LNCS Vol. 1423, Springer Verlag, 1998, pp 528--540. http://www.springerlink.com/content/kxujf1gue5p054qy/fulltext.pdf
  82. {\sc C. Heuberger, A. Peth\H o} and {\sc R.F. Tichy,} {\em Complete solution of parametrized Thue equations}, Acta Math. Inf. Univ. Ostraviensis {\bf 6} (1998), 93--113
  83. {\sc A. Peth\H o} and {\sc H.G. Zimmer,} {\em On a system of norm equations over cyclic cubic number fields,} Publ. Math. Debrecen, {\bf 53} (1998), 317--332. Download
  84. {\sc K. Nakamula} and {\sc A. Peth\H o,} {\em Squares in Binary Recurrence Sequences,} In: "Number Theory", Eds.: K. Gy\H{o}ry, A.Peth\H{o} and V.T. S\'os, Walter de Gruyter GmbH \& Co., Berlin-New York, 1998, pp. 409--421. Download
  85. {\sc M. Mignotte} and {\sc A. Peth\H{o}}, {\em On the diophantine equation $x^p-x=y^q-y$}, Publicacions Matematiques, 43 (1999), 207--216.
  86. {\sc A. Peth\H o} and {\sc H.G. Zimmer,} {\em $S-$ integer points on elliptic curves, theory and practice,} Proceedings Number Theory Conference in Graz, 1998, In: Algebraic Number Theory and Diophantine Analysis, Eds.: F.Halter-Koch and R.F. Tichy, Walter de Gruyter, 2000, 351--363.
  87. {\sc J. Demetrovics, A. Peth\H o} and {\sc L. R\'onyai}, {\em On $\pm 1$-representations of integers}, Acta Cybernetica, {\bf 14} (1999), 27--36. Download the document
  88. {\sc A. Dujella} and {\sc A. Peth\H o,} {\em A family of elliptic curves}, Publ. Math. Debrecen, 56 (2000), 321 - 325. Download
  89. {\sc E. Herrmann, A. Peth\H o} and {\sc H.G. Zimmer,} {\em On Fermat's quadruple equations}, Abh. Math. Sem. Univ. Hamburg, {\bf 69} (1999), 283--291.
  90. {\sc E. Herrmann},and {\sc A. Peth\H o}, {\em S-integer points on elliptic curves, notes to a paper of B.M.M. de Weger}, Journal de Th\'eorie Nombres de Bordeaux, 13 (2001), 443--451.
  91. {\sc Sh. Akiyama} and {\sc A. Peth\H o}, {\em On canonical number systems}, Theor. Comp. Sci., 270 (2002), 921--933. Download the document
  92. {\sc A. Peth\H o} and {\sc S. Schmitt}, {\em Elements with bounded height in number fields}, Periodica Mathematica Hungarica, 43 (2001), 31--41. Download
  93. {\sc A. Peth\H{o},} {\em Diophantine properties of linear recursive sequences. II.}, Acta. Math. Acad. Paed. Ny\'{\i}regyh\'aziensis, {\bf 17} (2001), 81-96. Download the document
  94. {\sc A. Peth\H{o},} {\em Index form surfaces and construction of elliptic curves over large finite fields}, In: Public-Key Cryptography and Computational Number Theory, Eds.: Kazimierz Alster, Jerzy Urbanowicz and Hugh C. Williams, Walter de Gruyter GmbH \& Co, Berlin, 2001, pp. 239--247. Download
  95. {\sc Sh. Akiyama, H. Brunotte} and {\sc A. Pethő}, {\em Cubic CNS polynomials, notes on a conjecture of W.J. Gilbert}, J. Math. Anal. and Appl., {\bf 281} (2003), 402--415. Download
  96. {\sc Cl. Fuchs, A. Pethő} and {\sc R.F. Tichy}, {\em On the diophantine equation $G_n(x) = G_m(P(x))$}, Monatshefte Math., {\bf 137} (2002), 173--196. Download the document
  97. {\sc V. Komornik, P. Loretti} and {\sc A. Pethő }, {\em The smallest univoque number is not isolated}, Publ. Math. Debrecen {\bf 62/3-4} (2003), 429—435. Download the document
  98. {\sc C. Heuberger, A. Pethő} and {\sc R.F. Tichy}, {\em Thomas' family of Thue equations over imaginary quadratic fields}, J. Symbolic Comp., {\bf 34} (2002), 437-449. Download
  99. {\sc A. Peth\H{o},} {\em Notes on $CNS$ polynomials and integral interpolation}, In: More Sets, Graphs and Numbers, Eds.: E Györy, G.O.H. Katona and L. Lovász, Bolyai Soc. Math. Stud., 15, Springer, Berlin, 2006. pp.301-315.Download the document
  100. {\sc S. Akiyama, T. Borb\'ely, H. Brunotte, A. Peth\H{o}} and {\sc J. Thuswaldner}, {\em On a generalization of the radix representation - a survey}, Fields Institute Communications, 41, 2004, 19-27. Download
  101. {\sc S. Akiyama, T. Borb\'ely, H. Brunotte, A. Peth\H{o}} and {\sc J. Thuswaldner}, {\em Generalized radix representations and dynamical systems I}, Acta Math. Hungar., {\bf 108 (3)} (2005), 207 - 238. Download the document
  102. {\sc A. B\'erczes, J. K\"odm\"on} and {\sc A. Peth\H{o}}, {\em A one-way function based on norm form equations}, Periodica Math. Hungar., {\bf 49} (2004), 1-13. Download the document
  103. {\sc Cl. Fuchs, A. Peth\H{o}} and {\sc R.F. Tichy}, {\em On the diophantine equation $G_{n}(x)=G_{m}(P(x))$: higher order linear recurrences}, Trans. Amer. Math. Soc., {\bf 355} (2003), 4657--4681. Download
  104. {\sc A. Peth\H o}, {\em Egy negyedrend\H u rekurz\'{\i}v sorozatcsal\'adr\'ol}, Acta Acad. Paed. Agriensis, Sect. Math., {\bf 30} (2003), 115-122. Download
  105. {\sc E. Herrmann, I. Járási} and {\sc A.Pethõ}, {\em Note on J.H.E. Cohn's paper "The Diophantine equation $x^n=Dy^2+1$"}, Acta Arith., {\bf 113} (2004), 69--76. Download
  106. {\sc Cl. Fuchs, A. Peth\H{o}} and {\sc R.F. Tichy}, {\em On the diophantine equation $G_{n}(x)=G_{m}(P(y))$ with $Q(x,y)=0$, in:Diphantine Approximation, Eds.:H.P. Schlickewei, K. Schmidt and R.F. Tichy, Springer Verlag Wien, 2008, 199-209. Download
  107. {\sc Cl. Fuchs} and  {\scA. Peth\H{o}}, {\em Effective bounds for the zeros of linear recurrences in function fields}, J. Th\'eorie Nombres de Bordeaux, {\bf 17} (2005), 749—766. Download
  108. {\sc A. B\'erczes} and {\sc A. Peth\H o}, {\em On norm form equations with solutions forming arithmetic progressions}, Publ. Math. Debrecen, {\bf 65} (2004), 281-290. Download
  109. {\sc K. Gyarmati, A. S\'ark\"ozy} and {\sc A. Peth\H{o}}, {\em On linear recursion and pseudorandomness}, Acta Arith., {\bf 118} (2005), 359 – 374. Download
  110. {\sc G. Barat, Ch. Frougny} and {\sc A. Peth\H{o}}, {\em On linear recurrent Mahler numbers}, Integers, {\bf 5} (2005) #A1, 17 pages. http://www.westga.edu/~integers/vol5-3.html
  111. {\sc A. Peth\H{o}}, {\em Connections between power integral bases and radix representations in algebraic number fields}, Proc. 2003 Nagoya Conf. "Yokoi-Chowla Conjecture and Related Problems", Eds.: S-i. Katayama, C. Levesque and T. Nakahara, Furukawa Total Pr. 2004, 115-125. Download
  112. {\sc S.~Akiyama, H.~Brunotte, A.~Peth\H{o} and {J.~M.~Thuswaldner},  {\em Generalized radix representations and dynamical systems II,} Acta Arith., {\bf 121} (2006), 21-61. Download the document
  113. {\sc S.~Akiyama, H.~Brunotte, A.~Peth\H{o} and {W.~Steiner},  {\em Remarks on a conjecture on certain integer sequences}, Periodica Mathematica Hungarica, {\bf 52} (2006), 1-17. . Download the document
  114. {\sc A. B\'erczes} and {\sc A. Peth\H o}, {\em Computational experiences on norm form equations with solutions forming arithmetic progressions}, Glasnik Math., {\bf 41} (2006), 1-8. . Download the document
  115. {\sc S. Akiyama, T. Borb\'ely, H. Brunotte, A. Peth\H{o}} and {\sc J. Thuswaldner}, {\bf Basic properties of shift radix systems}, Acta. Math. Acad. Paed. Ny\'{\i}regyh\'aziensis, {\bf 22} (2006), pp. 19-25  (electronic) Download
  116. {\sc A. B\'erczes, A. Peth\H o } and {\sc V. Ziegler}, {\em Parameterized Norm Form Equations with Arithmetic progressions}, J. Symbolic Comput. {\bf 41} (2006), 790--810. Download
  117. {\sc H. Brunotte, A. Huszti } and {\sc A. Peth\H{o}}, {\bf Bases of canonical number systems in quartic algebraic number fields}, J. Th\'eorie Nombres de Bordeaux, {\bf 18} (2006), 537-557. Download the document
  118. {\sc A. Peth\H o } and {\sc V. Ziegler}, {\em Arithmetic progressions on Pell equations}, J. Number Theory, {\bf 128} (2008), 1389-1409. Download the document
  119. {\sc P. Kirschenhofer, A. Peth\H o} and {\sc J. Thuswaldner,} {\em On a family of three term nonlinear integer recurrences}, Int. J. Number Theory, {\bf 4} (2008), 135-146. Download
  120. {\sc S. Akiyama, H. Brunotte, A. Peth\H{o}} and {\sc J. Thuswaldner},  {\em Generalized radix representations and dynamical systems III}, Osaka Journal of Mathematics, {\bf 45} (2008), 347—374. Download the document
  121. {\sc A. Dujella,  A. Peth\H o} and {\sc P. Tadi\'{c},} {\em On arithmetic progressions on Pellian equations}, Acta Math. Hungar., {\bf 120} (2008), 29-38. Download the document
  122. {\sc J.~Foll\'ath, A.~Huszti} and {\sc A.~Peth\H o}, {\em DESignIn asymmetric authentication system}, ICAI 2007, 55-64. Download the document
  123. {\sc A. B\'erczes, L. Hajdu} and {\sc A. Peth\H o }, {\em Arithmetic progressions in the solution sets of norm form equations}, Rocky Mountain J. Math., {\bf 40} (2010), 383--395. Download the document
  124. {\sc S. Akiyama, H. Brunotte} and {\sc A. Peth\H o }, {\em Reducible cubic CNS polynomials}, Periodica Math. Hungar. {\bf 55} (2007), 177-183. Download the document
  125. {\sc A. Peth\H o } and {\sc D. Sima} Eds., J. Universal Computer Science, {\bf 12} Issue 9 (2006). Download the document
  126. {\sc S. Akiyama, H. Brunotte, A. Peth\H{o}} and {\sc W. Steiner}, {\em Periodicity of certain piecewise affine planar maps}, Tsukuba J. Math., {\bf 32} (2008), 197-251. Download the document
  127. {\sc S. Akiyama, H. Brunotte, A. Peth\H{o}} and {\sc J. Thuswaldner}, {\em Generalized radix representations and dynamical systems IV}, Indag. Math. (N.S) {\bf 19} (2008), 333--348. Download the document
  128. {\sc A. Peth\H o }, {\em On the boundary of the closure of the set of contractive polynomials}, Integers, {\bf 9} (2009), 311–325. Download
  129. {\sc P. Kirschenhofer, A. Peth\H o, P. Surer} and {\sc J. Thuswaldner,} {\em Finite and periodic orbits of shift radix systems}, J. Th\’eorie Nombres de Bordeaux, {\bf 22} (2010), 421—448. Download the document
  130. {\sc C. Fuchs} and  {\sc A. Peth\H o}, {\em On composite rational functions having a bounded number of zeros and poles}, Proc. AMS to appear.
  131. {\sc C. Fuchs} and  {\sc A. Peth\H o}, {\em On composite rational functions having a bounded number of zeros and poles}, Proc. AMS to appear
  132. {\sc A. B\’erczes, J. Foll\’ath} and {\sc A. Peth\H o}, {\em On a family of collision-free functions}, to appear, Tatra Mountains Math. Publ.
  133. {\sc A. Peth\H o}, {\em Fifteen problems in number theory}, Acta Univ. Sap., Math. {\bf 2} (2010), 72—83. http://www.acta.sapientia.ro/acta-math/C2-1/math21-5.pdf
  134. {\sc A. Huszti} and {\sc A. Peth\H o}, {\em A secure electronic exam system}, Publ. Math. Debrecen, {\bf 77} (2010), 299—312.

 

 

Theses

1.       Normaforma egyenletek megold\'asainak eloszl\'as\'ar\'ol, doktori \'ertekez\'es, KLTE Debrecen, 1975.

2.       Normaforma egyenletek megold\'asainak \'es bizonyos tulajdons\'ag\'u algebrai sz\'amoknak az eloszl\'as\'ar\'ol, kandid\'atusi \'ertekez\'es, KLTE Debrecen, 1979.

3.     Diofantoszi egyenletek effektiv \'es explicit megold\'asa, akad\'emiai doktori \'ertekez\'es, KLTE Debrecen, 1990. Download the document

 

 

Reports and talks

1.       {\sc M. Mignotte} et {\sc A. Peth\H{o},} {\em Az $a^n+b^n=z^3$ diofantoszi egyenletr\H{o}l,} Acta Acad. Paed. Agriensis, Sect. Math. (1995-96), 45--53.

2.       {\sc Dr. Fazekasn\'e Kis M\'aria} \'es {\sc Peth\H{o} Attila}, {\em Integr\'alt eg\'eszs\'eg\"ugyi \'es gazdas\'agi inform\'aci\'os rendszerek \'ert\'ekel\'es\'enek fontosabb szempontjai a Debreceni Orvostudom\'anyi Egyetemen}, Eg\'eszs\'eg\"ugyi Gazdas\'agi Szemle, {\bf 32}(1994), 560--568.

3.       {\sc Peth\H{o} Attila, dr. Fazekasn\'e Kis M\'aria, Feh\'ert\'oi J\'anosn\'e} \'es {\sc Hadh\'azi Attila}, {\em Hogyan fejl\H{o}dik a DOTE sz\'am\'{\i}t\'og\'epes inform\'aci\'os rendszere?}, Lege Artis Medicinae,{\bf 5} (1995), 815--819.

4.     A. Pethő, On the solutions of parametrized families of diophantine equations, Debrecen, October 25, 2001. Download the document

5.     Pethő Attila, A Számítástudományi → Számítógéptudományi Tanszék első harminc éve, Debrecen, 2002. Augusztus 29. Download the document

6.     {\sc Attila Peth\H{o}}, Fr\"uchte einer langj\"ahrigen Zusammenarbeit, Festkolloquium H.G. Zimmer, 25. Oktober, 2002. Download the document

7.     {\sc Peth\H{o} Attila }, {\em Rekurz\'{\i}v polinomsorozatok}, a 2003 november 12.-én, tartott előadás szerkesztett változata. Download the document

8.     {\sc Attila Peth\H{o}}, On Generalized Radix Representations, Kyoto, October 1, 2003. Download the document

9.     {\sc Attila Peth\H{o}}, On norm form equations with solutions forming arithmetic progressions, Marseille, May 19, 2005. Download the document

10. {\sc Attila Peth\H{o}}, Units and Diophantine Equations; Dedicated to the 60th birthday of Michael Pohst, Berlin, June 10, 2005. . Download the document

11. {\sc Attila Peth\H{o}}, On diophantine equations with solutions forming arithmetic progressions, Klagenfurt, September 19, 2005 . Download the document

12. {\sc Attila Peth\H{o}}, Problems, Debrecen, January 29, 2009 . Download the document

 

 

 

 

 

 

 

 

Last update 31.12.2009, Attila Pethõ