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1999 | 90 | 1 | 17-35
Tytuł artykułu

Applications of a lower bound for linear forms in two logarithms to exponential Diophantine equations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
90
Numer
1
Strony
17-35
Opis fizyczny
Daty
wydano
1999
otrzymano
1996-12-10
poprawiono
1998-10-26
Twórcy
  • Division of General Education, Ashikaga Institute of Technology, 268-1 Omae, Ashikaga, Tochigi 326, Japan
Bibliografia
  • [BS] J. Browkin and A. Schinzel, On the equation $2^n - D = y^2$, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 311-318.
  • [B1] E. Brown, Diophantine equations of the form $x^2 + D = y^n$, J. Reine Angew. Math. 274/275 (1975), 385-389.
  • [B2] E. Brown, Diophantine equations of the form $ax^2 + Db^2 = y^n$, ibid. 291 (1977), 118-127.
  • [BG] Y. Bugeaud and K. Győry, Bounds for the solutions of Thue-Mahler equations and norm form equations, Acta Arith. 74 (1996), 273-292.
  • [Cao] Z. F. Cao, A note on the diophantine equation $a^x + b^y = c^z$, Acta Arith., to appear.
  • [Ca] J. W. S. Cassels, On the equation $a^x - b^y = 1$, Amer. J. Math. 75 (1953), 159-162.
  • [Co1] J. H. E. Cohn, Eight Diophantine equations, Proc. London Math. Soc. (3) 16 (1966), 153-166.
  • [Co2] J. H. E. Cohn, The diophantine equation $x^2 + 2^k = y^n$, Arch. Math. (Basel) 59 (1992), 341-344.
  • [Co3] J. H. E. Cohn, The diophantine equation $x^2 + C = y^n$, Acta Arith. 65 (1993), 367-381.
  • [GL] Y.-D. Guo and M.-H. Le, A note on Jeśmanowicz' conjecture concerning Pythagorean numbers, Comment. Math. Univ. St. Pauli 44 (1995), 225-228.
  • [G] R. Guy, Unsolved Problems in Number Theory, 2nd ed., Springer, 1994.
  • [J] L. Jeśmanowicz, Some remarks on Pythagorean numbers, Wiadom. Mat. 1 (1955/1956), 196-202 (in Polish).
  • [LMN] M. Laurent, M. Mignotte et Y. Nesterenko, Formes linéaires en deux logarithmes et déterminants d'interpolation, J. Number Theory 55 (1995), 285-321.
  • [Le] M.-H. Le, On Jeśmanowicz' conjecture concerning Pythagorean numbers, Proc. Japan Acad. Ser. A 72 (1996), 97-98.
  • [Lv] W. J. LeVeque, On the equation $a^x - b^y = 1$, Amer. J. Math. 74 (1952), 235-331.
  • [M] M. Mignotte, A corollary to a theorem of Laurent-Mignotte-Nesterenko, Acta Arith. 86 (1998), 101-111.
  • [MW] M. Mignotte and M. Waldschmidt, Linear forms in two logarithms and Schneider's method III, Ann. Fac. Sci. Toulouse Math. 97 (1989), 43-75.
  • [N1] T. Nagell, Sur l'impossibilité de quelques équations à deux indéterminées, Norsk. Mat. Forenings Skrigter 13 (1923), 65-82.
  • [N2] T. Nagell, Verallgemeinerung eines Fermatschen Satzes, Arch. Math. (Basel) 5 (1954), 153-159.
  • [N3] T. Nagell, Contributions to the theory of a category of diophantine equations of the second degree with two unknowns, Nova Acta Soc. Sci. Upsal. Ser. IV (2) 16 (1955), 1-38.
  • [N4] T. Nagell, Sur une classe d'équations exponentielles, Ark. Mat. 3 (1958), 569-582.
  • [P1] S. S. Pillai, On the inequality $0 < a^x - b^y ≤ n$, J. Indian Math. Soc. (1) 19 (1931), 1-11.
  • [P2] S. S. Pillai, On $a^x - b^y = c$, J. Indian Math. Soc. (2) 2 (1936), 19-122; Corr. J. Indian Math. Soc., 2, 215.
  • [Ra] S. Rabinowitz, On Mordell's equation $y^2 + k = x^3$ with $k = ±2^n3^m$, Doctoral dissertation at the City University of New York, 1971.
  • [Ri] P. Ribenboim, 13 Lectures on Fermat's Last Theorem, Springer, 1979.
  • [Sc] R. Scott, On the equations $p^x - b^y = c$ and $a^x + b^y = c^z$, J. Number Theory 44 (1993), 153-165.
  • [Si] W. Sierpi/nski, On the equation $3^x + 4^y = 5^z$, Wiadom. Mat. 1 (1955/1956), 194-195 (in Polish).
  • [Ta] K. Takakuwa, A remark on Jeśmanowicz' conjecture, Proc. Japan Acad. Ser. A 72 (1996), 109-110.
  • [Te1] N. Terai, The Diophantine equation $x^2 + q^m = p^n$, Acta Arith. 63 (1993), 351-358.
  • [Te2] N. Terai, The Diophantine equation $a^x + b^y = c^z$, Proc. Japan Acad. Ser. A 70 (1994), 22-26.
  • [Te3] N. Terai, The Diophantine equation $a^x + b^y = c^z$ II, ibid. 71 (1995), 109-110.
  • [Te4] N. Terai, The Diophantine equation $a^x + b^y = c^z$ III, ibid. 72 (1996), 20-22.
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Bibliografia
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