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On the integers represented by x4 − y4

Published online by Cambridge University Press:  17 April 2009

Andrzej Dąbrowski
Andrzej Dąbrowski
Affiliation:
Institute of Mathematics, University of Szczecin, ul. Wielkpolska 15, 70–451 Szczecin, Poland, e-mail: dabrowski@sus.univ.szczecin.pl
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Let p be a prime number ≥ 5, and n a positive integer > 1. This note is concerned with the diophantine equation x4 − y4 = nzp. We prove that, under certain conditions on n, this equation has no non-trivial solution in Z if p ≥ C(n), where C(n) is an effective constant.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 1 , August 2007 , pp. 133 - 136
Copyright
Copyright © Australian Mathematical Society 2007

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