@article{bwmeta1.element.bwnjournal-article-aav60i3p203bwm,
author = {Andrew Granville},
title = {Finding integers k for which a given Diophantine equation has no solution in kth powers of integers},
journal = {Acta Arithmetica},
volume = {62},
year = {1992},
pages = {203-212},
zbl = {0725.11015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav60i3p203bwm}
}
Andrew Granville. Finding integers k for which a given Diophantine equation has no solution in kth powers of integers. Acta Arithmetica, Tome 62 (1992) pp. 203-212. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav60i3p203bwm/
[000] [AHB] L. M. Adleman and D. R. Heath-Brown, The first case of Fermat's last theorem, Invent. Math. 79 (1985), 409-416. | Zbl 0557.10034
[001] [An] N. C. Ankeny, The insolubility of sets of Diophantine equations in the rational numbers, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 880-884. | Zbl 0047.27602
[002] [AE] N. C. Ankeny and P. Erdős, The insolubility of classes of Diophantine equations, Amer. J. Math. 76 (1954), 488-496. | Zbl 0056.03505
[003] [BM] W. D. Brownawell and D. W. Masser, Vanishing sums in function fields, Math. Proc. Cambridge Philos. Soc. 100 (1986), 427-434. | Zbl 0612.10010
[004] [Ch] V. Chvátal, Linear Programming, Freeman, New York 1983.
[005] [CJ] J. H. Conway and A. J. Jones, Trigonometric diophantine equations (On vanishing sums of roots of unity), Acta Arith. 30 (1976), 229-240. | Zbl 0349.10014
[006] [DL] H. Davenport and D. J. Lewis, Homogeneous additive equations, Proc. Royal Soc. Ser. A 274 (1963), 443-460. | Zbl 0118.28002
[007] [Fa] G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), 349-366, Erratum, Proc. Royal Soc. Ser. A 75 (1984), 381.
[008] [Fo] E. Fouvry, Théorème de Brun-Titchmarsh; application au théorème de Fermat, Proc. Royal Soc. Ser. A 79 (1985), 383-407. | Zbl 0557.10035
[009] [G1] A. Granville, Diophantine equations with varying exponents (with special reference to Fermat's Last Theorem), Doctoral thesis, Queen's University, Kingston, Ontario, 1987, 209 pp.
[010] [G2] A. Granville, Some conjectures in Analytic Number Theory and their connection with Fermat's Last Theorem, in: Analytic Number Theory, B. C. Brendt, H. G. Diamond, H. Halberstam, A. Hildebrand (eds.) Birkhäuser, Boston 1990, 311-326.
[011] [G3] A. Granville, The set of exponents for which Fermat's Last Theorem is true, has density one, C. R. Math. Acad. Sci. Canada 7 (1985), 55-60. | Zbl 0565.10016
[012] [HB] D. R. Heath-Brown, Fermat's Last Theorem for ``almost all'' exponents, Bull. London Math. Soc. 17 (1985), 15-16. | Zbl 0546.10012
[013] [L] H. W. Lenstra,Jr., Vanishing sums of roots of unity, in: Proc. Bicentennial Cong. Wiskundig Genootschap, Vrije Univ., Amsterdam 1978, 249-268.
[014] [M] H. B. Mann, On linear relations between roots of unity, Mathematika 12 (1965), 107-117. | Zbl 0138.03102
[015] [NS] D. J. Newman and M. Slater, Waring's problem for the ring of polynomials, J. Number Theory 11 (1979), 477-487. | Zbl 0407.10039
[016] [Ri] P. Ribenboim, An extension of Sophie Germain's method to a wide class of diophantine equations, J. Reine Angew. Math. 356 (1985), 49-66. | Zbl 0546.10013
[017] [V] H. S. Vandiver, On classes of Diophantine equations of higher degrees which have no solutions, Proc. Nat. Acad. Sci., U.S.A. 32 (1946), 101-106. | Zbl 0063.07966