本文的目的是解决一个素数为特殊形式的六元丢番图不等式.更准确地说,令1 ≤ c ≤1831/1264是一个固定的实数,N是一个充分大的正数并且e表示一个较小的正常数.我们证明了丢番图不等式|pc1+pc2+…+pc6-N|＜ε 在素变量 p1,p2,…,p6 上有解,并且使得 p1=x2+y2+1,这时 x和y为整数.
A Diophantine inequality with one prime of the form p=x2+y2+1
Our aim of this paper is to solve the Diophantine inequality with six prime numbers of a special form.More precisely,let 1＜c＜1831/1264 be a fixed real number,N be a sufficiently large positive number and ε denote a small positive constant.We prove that the Diophantine inequality|pc1+pc2+…+pc6-N|＜ε is solvable in prime variables p1,p2,…,p6 such that p1=x2+y2+1 with integers x and y.
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