Classical and modular approaches to exponential Diophantine equations I . Fibonacci

  title={Classical and modular approaches to exponential Diophantine equations I . Fibonacci},
  author={Maurice Mignotte and Samir Siksek},
This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat’s Last Theorem. In this paper we give new improved bounds for linear forms in three logarithms. We also apply a combination of classical techniques with the modular approach to show that the only perfect powers in the Fibonacci sequence are 0, 1, 8 and… CONTINUE READING
Highly Cited
This paper has 64 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.
35 Citations
55 References
Similar Papers


Publications citing this paper.

64 Citations

Citations per Year
Semantic Scholar estimates that this publication has 64 citations based on the available data.

See our FAQ for additional information.


Publications referenced by this paper.
Showing 1-10 of 55 references

An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers

  • E. M. Matveev
  • II, Izv. Ross. Akad. Nauk Ser. Mat. 64 (2000…
  • 2000
Highly Influential
5 Excerpts

Links between stable elliptic curves and certain Diophantine equations

  • G. Frey
  • Ann. Univ. Sarav. Ser. Math. 1
  • 1986
Highly Influential
18 Excerpts


  • W. Bosma
  • Cannon and C. Playoust: The Magma Algebra System…
  • 1997
Highly Influential
6 Excerpts

Linear forms in the logarithms of three positive rational numbers

  • C. D. Bennett, J. Blass, A.M.W. Glass, D. B. Meronk, R. P. Steiner
  • J. Théor. Nombres Bordeaux 9
  • 1997
Highly Influential
6 Excerpts

Algorithms for modular elliptic curves

  • J. E. Cremona
  • 2nd edition, Cambridge University Press
  • 1996
Highly Influential
4 Excerpts

Bounds for the solutions of Thue-Mahler equations and norm form equations

  • Y. Bugeaud, K. Győry
  • Acta. Arith. 74
  • 1996
Highly Influential
10 Excerpts

Formes linéares en deux logarithmes et déterminants d’interpolation

  • M. Laurent, M. Mignotte, Y. Nesterenko
  • J. Number Theory 55
  • 1995
Highly Influential
8 Excerpts

Perfect powers in second order recurrences

  • A. Pethő
  • in: Topics in Classical Number Theory…
  • 1984
Highly Influential
11 Excerpts

Similar Papers

Loading similar papers…