Addendum to the paper:

A. Schinzel

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Displaying similar documents to “Addendum to the paper:'On two theorems of Gelfond and some of their applications' (Acta Arith. 13 (1967), pp. 177-236)”

On the diophantine equation x - x = y - y.

Maurice Mignotte, Attila Petho (1999)

Publicacions Matemàtiques

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We consider the diophantine equation (*) x^p - x = y^q - y in integers (x, p, y, q). We prove that for given p and q with 2 ≤ p < q, (*) has only finitely many solutions. Assuming the abc-conjecture we can prove that p and q are bounded. In the special case p = 2 and y a prime power we are able to solve (*) completely.