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A note on Jeśmanowicz' conjecture concerning Pythagorean triples

Published online by Cambridge University Press:  17 April 2009

Maohua Le
Department of MathematicsZhanjiang Normal CollegePostal Code 524048, Zhanjiang, Guangdong, People's Republic of China
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Let n be a positive integer, and let (a, b, c) be a primitive Pythagorean triple. In this paper we give certain conditions for the equation (an)x + (bn)y = (cn)z to have positive integer solutions (x, y, z) with (x, y, z) ≠ (2, 2, 2). In particular, we show that x, y and z must be distinct.

Research Article
Copyright © Australian Mathematical Society 1999


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