3个素数平方和的非线性型的整数部分

假设λ,μ,υ是不全为负的非零实数,λ是无理数,k是正整数,则存在无穷多素数p_1,p_2,p_,p,3使得λp_1~2+μp_2~2+υp_3~2]=kp.特别地,λp_1~2+μp_2~2+υp_3~2]表示无穷多素数.

Integral Part of a Nonlinear Form with Three Squares of Primes

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.