关于不同素数幂之和的特殊集合的说明

Indian Journal of Pure and Applied Mathematics Pub Date : 2024-09-13 DOI:10.1007/s13226-024-00695-0

Yuhui Liu

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摘要

本文证明了，只要有(O(N^{\frac{13}{96}+\varepsilon })\)个例外，每个满足\(n\leqslant N\), \(n\not \equiv 2\,(\textrm{mod}\,3)\) 的足够大的偶整数都可以表示为两个素数的平方、一个素数的立方和三个素数的双四次方的和。这一结果是对作者[6]结果的改进。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A note on the exceptional set for sums of unlike powers of primes

In this paper, it is proved that with at most \(O(N^{\frac{13}{96}+\varepsilon })\) exceptions, every sufficiently large even integer satisfying \(n\leqslant N\), \(n\not \equiv 2\,(\textrm{mod}\,3)\) can be represented as the sum of two squares of primes, one cube of primes and three biquadrates of primes. This result constitutes a refinement upon that of the author [6].

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Indian Journal of Pure and Applied Mathematics

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