# Math Help - Integer solutions to equation p^3=q^2

1. ## Integer solutions to equation p^3=q^2

Hi, I am wondering if there are solutions to the equation p^2 = q^3, where p and q are integers (ignoring zero and one). If so, can someone give me a hint on how to find them. If not, can someone show me a proof that this is the case?

2. Originally Posted by borophyll
Hi, I am wondering if there are solutions to the equation p^2 = q^3, where p and q are integers (ignoring zero and one). If so, can someone give me a hint on how to find them. If not, can someone show me a proof that this is the case?

$8^2=4^3\,,\,27^2=9^3\,,\,125^2=25^3$ ...can you see a pattern here?

Tonio

3. Originally Posted by tonio
$8^2=4^3\,,\,27^2=9^3\,,\,125^2=25^3$ ...can you see a pattern here?

Tonio
ah of course, $(n^2)^3 = (n^3)^2$, for any n

How could I be so dumb?