A Note on the Diophantine Equation $x^2 + y^6 = z^e$, $e \geq 4$
Printed: Jun 2012
We consider the diophantine equation $x^2 + y^6 = z^e$, $e \geq 4$.
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
11D - unknown classification 11D