Determine all possible integer solutions, whether positive or negative, to this equation:

5y⁴ + 2560y² = x⁵ - 65536

(In reply to Small steps by Gamer)

5*(y² + 256)² = x⁵ + 2^18

implies x^5 + 2^18 is a multiple of 5.

2^18 is congruent to 4 mod 5, so x^5 is congruent to 1 mod 5.

This implies x is congruent to 1 mod 5.

The known solution x=16 fits this, but I'm stuck.

Posted by Jer on 2006-03-16 12:53:05