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A Note on the Diophantine Equation x2 + y6 = ze, e ≥ 4
Published online by Cambridge University Press: 20 November 2018
Abstract
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We consider the diophantine equation 
${{x}^{2}}\,+\,{{y}^{6}}\,=\,{{z}^{e}},\,e\,\le \,4$. We show that, when 
$e$ is a multiple of 4 or 6, this equation has no solutions in positive integers with 
$x$ and 
$y$ relatively prime. As a corollary, we show that there exists no primitive Pythagorean triangle one of whose leglengths is a perfect cube, while the hypotenuse length is an integer square.
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- Research Article
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- Copyright © Canadian Mathematical Society 2012
References
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