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UNE CONJECTURE DE LEBESGUE
Published online by Cambridge University Press: 29 March 2004
Abstract
Let $A > 0$ be an integer. The equation $x^5 - y^5 = Az^5$ was first studied by Dirichlet and Lebesgue. Lebesgue conjectured in 1843 that if $A$ has no prime divisors of the form $10k+1$, the equation has no solutions except the visible ones. Partial results were obtained by Lebesgue and by Terjanian in 1987. The purpose of the paper is to prove Lebesgue's conjecture. The main tool used is the method known as the elliptic Chabauty method.
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- The London Mathematical Society 2004
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