Some identities involving primes

Published in: Quaestiones Mathematicae
Volume 40, issue 8, 2017 , pages: 1127–1134
DOI: 10.2989/16073606.2017.1367334
Author(s): Yuhui LiuSchool of Mathematics, P.R. China


The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study some classical problem related to a prime p. We shall give some new identities involving a prime p, one of which is that if prime p = 6k + 1, then there exist three positive integers x, y and z such that p2 = x2 + y2 + z2. At the same time, we also give an exact expression for x, y and z.

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