Question 89707
Good luck on this!
Prove that there are no solutions for: {{{x^4+y^4 = 625}}} 
This can be written as:
{{{x^4+y^4 = z^4}}} where z = 5
Refer to Fermat's last theorem:
{{{x^n+y^n = z^n}}} There are no solutions for n>2

You might contact Andrew Wile for his thoughts on this.