一个二元丢番图不等式(英文)  

On a Binary Diophantine Inequality

作　　者：翟文广[1] 曹晓东[2] 

机构地区：[1]山东师范大学数学系,济南山东中国250014 [2]北京石油化工学院数理部,北京中国102600

出　　处：《数学进展》2003年第6期706-721,共16页Advances in Mathematics（China）

基　　金：This work is sunpported by the National Natural Science Foundation(No.19801021);National Natural Science foundation of Shandong Province(Grand No.Q98A02110)

摘　　要：本文证明了如果1<c<43/36,则二元素变数丢番图不等式|P_1~c+P_2~c-N|<N^(1-43/36c)对几乎所有的正数N是可解的,改进了Laporta的结果1<c<15/14。我们也研究了番图不等式|P^c+P_k^c-N|<ε对于充分大的正数N的可解性问题,这里p是素数,而P_k表示最多有k个素因子的正整数,ε为一充分小的正数。In this paper we prove that if 1 < c < 43/36,then the Diopantine inequality |P1c + p2c - N| < N1-43/36c is solvable in prime numbers p1 and p2 for 'almost all' N > 0, which improves Laporta's range 1 < c < 15/14. For sufficiently large N, we also investigate the solvable of the Diophantine inequality |pc + Pkc - N|< ε in a prime p and a positive integer Pk with at most k prime factors.

关 键 词：丢番图不等式 可解性 素数 正整数 

分 类 号：O156.7[理学—数学]