## Equation : a^4 – b^5 = c^5 – d^4

Let   $a, \; b, \; c, \; d$   be positive integers,   with   $a \; \neq \; d$,   and   $b \; \neq \; c$

Prove that if   $a^4-b^5=c^5-d^4$,   then twice the sum of the 5-th powers is a sum of two squares.