On monochromatic sums of squares of primes

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• 作者：Guohua Chen ^{guohuachen@mail.sdu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11P32 ; 11P55
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：162
• 期：Complete
• 页码：180-189
• 全文大小：283 K

文摘

Let K   be a positive integer, $\{A_i,1\le i\le K\}$ be any partition of the sequence of squares of primes and a280892f82" title="Click to view the MathML source">s(K)$s(K)$ be the smallest positive integer such that every sufficiently large integer can be written as the sum of no more than a280892f82" title="Click to view the MathML source">s(K)$s(K)$ elements, which belong to one of the sets A_i$A_i$. In this paper, we prove that s(K)≪_ϵK^2+ϵ$s(K){\ll }_{ϵ}{K}^{2+ϵ}$ for sufficiently small positive number ϵ   and all K≥1$K\ge 1$.