Some identities involving primes

  • Yuhui Liu
Keywords: Gauss sums, the equation related to primes, solutions, analytic method.

Abstract

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.

Mathematics Subject Classification (2010): 11L05, 11P32.
Key words: Gauss sums, the equation related to primes, solutions, analytic method.

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Articles

Journal Identifiers


eISSN: 1727-933X
print ISSN: 1607-3606