Equal Sums of Four Even Powers

Abstract

Let u, v, w, z,  k, m and I be any integers such that k = z - w = w - v = v - u . The study of integer I for which I = u2n + v2n + w2n + z2n = k2 + m2 + r2 is not known. This study is therefore, set to partially overcome this challenge by introducing new formula relating sums of four even powers as an exact sum of three squares.