Two Diophantine equation generator function for integer residuals produced by integer division over closed intervals are presented. One each for the closed intervals 1, √ and √ , , respectively.

In this paper we obtain a parametric solution of the hitherto unsolved diophantine equation $(x_1^5+x_2^5)(x_3^5+x_4^5)=(y_1^5+y_2^5)(y_3^5+y_4^5)$. Further, show, using elliptic curves, that there exist infinitely many solutions aforementioned equation, and they can be effectively computed.