Finding integers k for which a given Diophantine equation has no solution in kth powers of integers

Andrew Granville

Acta Arithmetica (1992)

  • Volume: 60, Issue: 3, page 203-212
  • ISSN: 0065-1036

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Andrew Granville. "Finding integers k for which a given Diophantine equation has no solution in kth powers of integers." Acta Arithmetica 60.3 (1992): 203-212. <http://eudml.org/doc/206435>.

@article{AndrewGranville1992,
author = {Andrew Granville},
journal = {Acta Arithmetica},
language = {eng},
number = {3},
pages = {203-212},
title = {Finding integers k for which a given Diophantine equation has no solution in kth powers of integers},
url = {http://eudml.org/doc/206435},
volume = {60},
year = {1992},
}

TY - JOUR
AU - Andrew Granville
TI - Finding integers k for which a given Diophantine equation has no solution in kth powers of integers
JO - Acta Arithmetica
PY - 1992
VL - 60
IS - 3
SP - 203
EP - 212
LA - eng
UR - http://eudml.org/doc/206435
ER -

References

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  1. [AHB] L. M. Adleman and D. R. Heath-Brown, The first case of Fermat's last theorem, Invent. Math. 79 (1985), 409-416. Zbl0557.10034
  2. [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. Zbl0047.27602
  3. [AE] N. C. Ankeny and P. Erdős, The insolubility of classes of Diophantine equations, Amer. J. Math. 76 (1954), 488-496. Zbl0056.03505
  4. [BM] W. D. Brownawell and D. W. Masser, Vanishing sums in function fields, Math. Proc. Cambridge Philos. Soc. 100 (1986), 427-434. Zbl0612.10010
  5. [Ch] V. Chvátal, Linear Programming, Freeman, New York 1983. 
  6. [CJ] J. H. Conway and A. J. Jones, Trigonometric diophantine equations (On vanishing sums of roots of unity), Acta Arith. 30 (1976), 229-240. Zbl0349.10014
  7. [DL] H. Davenport and D. J. Lewis, Homogeneous additive equations, Proc. Royal Soc. Ser. A 274 (1963), 443-460. Zbl0118.28002
  8. [Fa] G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), 349-366, Erratum, Proc. Royal Soc. Ser. A 75 (1984), 381. 
  9. [Fo] E. Fouvry, Théorème de Brun-Titchmarsh; application au théorème de Fermat, Proc. Royal Soc. Ser. A 79 (1985), 383-407. Zbl0557.10035
  10. [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. 
  11. [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. 
  12. [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. Zbl0565.10016
  13. [HB] D. R. Heath-Brown, Fermat's Last Theorem for ``almost all'' exponents, Bull. London Math. Soc. 17 (1985), 15-16. Zbl0546.10012
  14. [L] H. W. Lenstra,Jr., Vanishing sums of roots of unity, in: Proc. Bicentennial Cong. Wiskundig Genootschap, Vrije Univ., Amsterdam 1978, 249-268. 
  15. [M] H. B. Mann, On linear relations between roots of unity, Mathematika 12 (1965), 107-117. Zbl0138.03102
  16. [NS] D. J. Newman and M. Slater, Waring's problem for the ring of polynomials, J. Number Theory 11 (1979), 477-487. Zbl0407.10039
  17. [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. Zbl0546.10013
  18. [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. Zbl0063.07966

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