We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
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.
