On a criterion for Catalan's Conjecture

Abstract

We give a new proof of a theorem by P. Mihailescu which states that the equation $x^p-y^q=1$ is unsolvable with $x,y$ integral and $p,q$ odd primes, unless the congruences $p^q\equiv p(\mathrm{mod}{q}^2)$ and $q^p\equiv q(\mathrm{mod}{p}^2)$ hold.

Cited by in corpus (1)

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