The non-homogeneous heptic equation with five unknowns equation

Abstract

The non-homogeneous Heptic equation with five unknowns given by equation is considered and analyzed for its non– zero distinct integer solutions. To solve this higher degree Diophantine equation, we have employed techniques such as brute force method and substitution strategy. A few interesting relations between the solutions and special numbers namely, polygonal numbers, pyramidal numbers and centered pyramidal numbers.