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1995 Catalan's equation has no new solution with either exponent less than 10651
Maurice Mignotte, Yves Roy
Experiment. Math. 4(4): 259-268 (1995).

Abstract

We consider Catalan's equation $x^p-y^q=1$ (where all variables are integers and $p,q$ are greater than $1$), which has the obvious solution $9-8=1$. Are there others? Applying old and new theoretical results to a systematic computation, we were able to improve on recent work of Mignotte and show that Catalan's equation has only the obvious solutions when $\min\{p,q\}<10651$. Two crucial tools used are a new result of Laurent, Mignotte, and Nesterenko on linear forms of logarithms, and a criterion obtained by W. Schwarz in 1994.

Citation

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Maurice Mignotte. Yves Roy. "Catalan's equation has no new solution with either exponent less than 10651." Experiment. Math. 4 (4) 259 - 268, 1995.

Information

Published: 1995
First available in Project Euclid: 14 March 2003

zbMATH: 0857.11012
MathSciNet: MR1387692

Subjects:
Primary: 11D61
Secondary: 11J86

Rights: Copyright © 1995 A K Peters, Ltd.

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Vol.4 • No. 4 • 1995
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