Waring-Goldbach problems for one square and higher powers

TL;DR

This paper proves new results in additive number theory, showing that large integers can be expressed as sums involving one square and multiple prime-powered terms, advancing understanding of prime representations.

Contribution

It establishes that large odd integers are sums of one prime square and fourteen fifth powers, and even integers as sums of one prime square, one biquadrate, and twelve fifth powers, with all terms prime.

Findings

Large odd integers as sums of one prime square and fourteen fifth powers.

Large even integers as sums of one prime square, one biquadrate, and twelve fifth powers.

All terms in the representations are primes.

Abstract

We prove that every sufficiently large odd integer can be expressed as a sum of one square and fourteen fifth powers, all of primes. In addition, we establish that every sufficiently large even integer can be written as a sum of one square, one biquadrate, and twelve fifth powers of primes.