# Question on Fermat's Last Theorem

Wiz14
According to Fermat's last theorem, a 6th power plus a 6th power cannot equal a 6th power, but a square plus a square can equal a square. But can't 6th powers be written as squares of 3rd powers? Also, can't any even powers be written as squares?

Staff Emeritus
Homework Helper
But can't 6th powers be written as squares of 3rd powers? Also, can't any even powers be written as squares?

Yes, they can be written as such. Not really sure what you're getting at...

Wiz14
Yes, they can be written as such. Not really sure what you're getting at...

Is this a way to know what numbers cannot be pythagorean triples? for example:
a2 + b2 = c2
cannot have integer solutions if a,b, and c are perfect squares, cubes, fourth powers, etc?