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.
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Kimtai Boaz Simatwo (2024) studied this question.
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