The integer part of nonlinear forms with prime variables

Abstract

<abstract><p>In this paper, we discuss problems that integer part of nonlinear forms with prime variables represent primes infinitely. We prove that under suitable conditions there exist infinitely many primes $ p_j, p $ such that $ [\lambda_1p_1^2+\lambda_2p_2^2+\lambda_3p_3^k] = p $ and $ [\lambda_1p_1^3+\cdots+\lambda_4p_4^3+\lambda_5p_5^k] = p $ with $ k\geq 2 $ and $ k\geq 3 $ respectively, which improve the author's earlier results.</p></abstract>