Asian Research Journal of Mathematics

Equal Sums of Four Even Powers

Kimtai Boaz Simatwo *

Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya.

*Author to whom correspondence should be addressed.

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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.

Keywords: sums of three squares, sums of four even powers

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