## Taiwanese Journal of Mathematics

### Exceptional Set for Sums of Unlike Powers of Primes

#### Abstract

Let $N$ be a sufficiently large integer. In this paper, it is proved that with at most $O(N^{13/16+\varepsilon})$ exceptions, all even positive integers up to $N$ can be represented in the form $p_1^2 + p_2^2 + p_3^3 + p_4^3 + p_5^4 + p_6^4$, where $p_1$, $p_2$, $p_3$, $p_4$, $p_5$, $p_6$ are prime numbers.

#### Article information

Source
Taiwanese J. Math., Volume 22, Number 4 (2018), 779-811.

Dates
Accepted: 26 September 2017
First available in Project Euclid: 14 October 2017

https://projecteuclid.org/euclid.twjm/1507946425

Digital Object Identifier
doi:10.11650/tjm/170906

Mathematical Reviews number (MathSciNet)
MR3830821

Zentralblatt MATH identifier
06965397

#### Citation

Zhang, Min; Li, Jinjiang. Exceptional Set for Sums of Unlike Powers of Primes. Taiwanese J. Math. 22 (2018), no. 4, 779--811. doi:10.11650/tjm/170906. https://projecteuclid.org/euclid.twjm/1507946425

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