论文标题
用$ p = x^2+y^2+1 $的一个素数的二芬太汀近似
Diophantine approximation with one prime of the form $p=x^2+y^2+1$
论文作者
论文摘要
令$ \ varepsilon> 0 $为一个小常数。在本文中，我们证明，每当$η$都是真实的，并且常数$λ_i$满足某些必要条件，那么就存在无限的许多素数$ p_1，\，\，\，p_2，\，p_3 $满足不平等\ begin {equination {equation*} \ end {equation*}，使得$ p_3 = x^2 + y^2 + 1 $。
Let $\varepsilon>0$ be a small constant. In the present paper we prove that whenever $η$ is real and constants $λ_i$ satisfy some necessary conditions, then there exist infinitely many prime triples $p_1,\, p_2,\, p_3$ satisfying the inequality \begin{equation*} |λ_1p_1 + λ_2p_2 + λ_3p_3+η|<\varepsilon \end{equation*} and such that $p_3=x^2 + y^2 +1$.
