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An exponential diophantine equation

Published online by Cambridge University Press:  17 April 2009

Maohua Le
Department of Mathmatics, Zhanjiang Normal College, Postal code 524048, Zhanjiang, Guangdong, People's Republic of China
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Let p be an odd prime with p > 3. In this paper we give all positive integer solutions (x, y, m, n) of the equation x2 + p2m = yn, gcd (x, y) = 1, n > 2 satisfying 2 | n of 2 ∤ n and p ≢ (−1)(p−1)/2(mod 4n.

Research Article
Copyright © Australian Mathematical Society 2001


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