Applications of a lower bound for linear forms in two logarithms to exponential Diophantine equations
Nobuhiro Terai
Acta Arithmetica, Tome 89 (1999), p. 17-35 / Harvested from The Polish Digital Mathematics Library
Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:207311
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     author = {Nobuhiro Terai},
     title = {Applications of a lower bound for linear forms in two logarithms to exponential Diophantine equations},
     journal = {Acta Arithmetica},
     volume = {89},
     year = {1999},
     pages = {17-35},
     zbl = {0933.11013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav90i1p17bwm}
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Nobuhiro Terai. Applications of a lower bound for linear forms in two logarithms to exponential Diophantine equations. Acta Arithmetica, Tome 89 (1999) pp. 17-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav90i1p17bwm/

[000] [BS] J. Browkin and A. Schinzel, On the equation 2n-D=y2, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 311-318. | Zbl 0095.26204

[001] [B1] E. Brown, Diophantine equations of the form x2+D=yn, J. Reine Angew. Math. 274/275 (1975), 385-389.

[002] [B2] E. Brown, Diophantine equations of the form ax2+Db2=yn, ibid. 291 (1977), 118-127.

[003] [BG] Y. Bugeaud and K. Győry, Bounds for the solutions of Thue-Mahler equations and norm form equations, Acta Arith. 74 (1996), 273-292. | Zbl 0861.11024

[004] [Cao] Z. F. Cao, A note on the diophantine equation ax+by=cz, Acta Arith., to appear.

[005] [Ca] J. W. S. Cassels, On the equation ax-by=1, Amer. J. Math. 75 (1953), 159-162. | Zbl 0050.03703

[006] [Co1] J. H. E. Cohn, Eight Diophantine equations, Proc. London Math. Soc. (3) 16 (1966), 153-166. | Zbl 0136.02806

[007] [Co2] J. H. E. Cohn, The diophantine equation x2+2k=yn, Arch. Math. (Basel) 59 (1992), 341-344. | Zbl 0770.11019

[008] [Co3] J. H. E. Cohn, The diophantine equation x2+C=yn, Acta Arith. 65 (1993), 367-381.

[009] [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. | Zbl 0849.11036

[010] [G] R. Guy, Unsolved Problems in Number Theory, 2nd ed., Springer, 1994. | Zbl 0805.11001

[011] [J] L. Jeśmanowicz, Some remarks on Pythagorean numbers, Wiadom. Mat. 1 (1955/1956), 196-202 (in Polish). | Zbl 0074.27205

[012] [LMN] M. Laurent, M. Mignotte et Y. Nesterenko, Formes linéaires en deux logarithmes et déterminants d'interpolation, J. Number Theory 55 (1995), 285-321.

[013] [Le] M.-H. Le, On Jeśmanowicz' conjecture concerning Pythagorean numbers, Proc. Japan Acad. Ser. A 72 (1996), 97-98. | Zbl 0876.11013

[014] [Lv] W. J. LeVeque, On the equation ax-by=1, Amer. J. Math. 74 (1952), 235-331.

[015] [M] M. Mignotte, A corollary to a theorem of Laurent-Mignotte-Nesterenko, Acta Arith. 86 (1998), 101-111. | Zbl 0919.11051

[016] [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. | Zbl 0702.11044

[017] [N1] T. Nagell, Sur l'impossibilité de quelques équations à deux indéterminées, Norsk. Mat. Forenings Skrigter 13 (1923), 65-82.

[018] [N2] T. Nagell, Verallgemeinerung eines Fermatschen Satzes, Arch. Math. (Basel) 5 (1954), 153-159. | Zbl 0055.03608

[019] [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.

[020] [N4] T. Nagell, Sur une classe d'équations exponentielles, Ark. Mat. 3 (1958), 569-582. | Zbl 0083.03902

[021] [P1] S. S. Pillai, On the inequality 0<ax-byn, J. Indian Math. Soc. (1) 19 (1931), 1-11.

[022] [P2] S. S. Pillai, On ax-by=c, J. Indian Math. Soc. (2) 2 (1936), 19-122; Corr. J. Indian Math. Soc., 2, 215.

[023] [Ra] S. Rabinowitz, On Mordell’s equation y2+k=x3 with k=±2n3m, Doctoral dissertation at the City University of New York, 1971.

[024] [Ri] P. Ribenboim, 13 Lectures on Fermat's Last Theorem, Springer, 1979. | Zbl 0456.10006

[025] [Sc] R. Scott, On the equations px-by=c and ax+by=cz, J. Number Theory 44 (1993), 153-165.

[026] [Si] W. Sierpi/nski, On the equation 3x+4y=5z, Wiadom. Mat. 1 (1955/1956), 194-195 (in Polish).

[027] [Ta] K. Takakuwa, A remark on Jeśmanowicz' conjecture, Proc. Japan Acad. Ser. A 72 (1996), 109-110. | Zbl 0863.11025

[028] [Te1] N. Terai, The Diophantine equation x2+qm=pn, Acta Arith. 63 (1993), 351-358.

[029] [Te2] N. Terai, The Diophantine equation ax+by=cz, Proc. Japan Acad. Ser. A 70 (1994), 22-26. | Zbl 0812.11024

[030] [Te3] N. Terai, The Diophantine equation ax+by=cz II, ibid. 71 (1995), 109-110.

[031] [Te4] N. Terai, The Diophantine equation ax+by=cz III, ibid. 72 (1996), 20-22.