| 李伟平,王天泽.3个素数平方和的非线性型的整数部分[J].数学年刊A辑,2011,32(6):753~762 |
| 3个素数平方和的非线性型的整数部分 |
| Integral Part of a Nonlinear Form with Three Squares of Primes |
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| DOI： |
| 中文关键词: 素数 非线性型 Davenport-Heilbronn方法 |
| 英文关键词:Prime Nonlinear form Davenport-Heilbronn method |
| 基金项目:国家自然科学基金(No11071070); 河南省教育厅自然科学研究计划(No2011B110002)资助的项目 |
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| 中文摘要: |
| 假设$\lambda, \mu, \nu$是不全为负的非零实数,$\lambda$是
无理数,$k$是正整数,则存在无穷多素数$p_1, p_2, p_3, p$,使得
$$
[\lambda p_1^2+\mu p_2^2+\nu p_3^2]=kp.
$$
特别地,$[\lambda p_1^2+\mu p_2^2+\nu p_3^2]$表示无穷多素数. |
| 英文摘要: |
| It is shown that if $\lambda,\mu,\nu$ are non-zero real numbers,
at least one of which is non-negative, $\lambda$ is irrational, and $k$ is a positive integer, then there exist
infinite primes $p_1, p_2, p_3, p$, such that
$$
[\lambda p_1^2+\mu p_2^2+\nu p_3^2]=kp.
$$
In particular,
$[\lambda p_1^2+\mu p_2^2+\nu p_3^2]$ represents infinite primes. |
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