有关殆素数的二元丢番图不等式  

A Binary Diophantine Inequality Involving Almost Primes

作　　者：李三华[1] 吴高翔[1] LI Sanhua;WU Gaoxiang(College of Mathematics and Physics,Jinggangshan University,Jibn 343009,Jiangxi,China)

机构地区：[1]井冈山大学数理学院,江西吉安343009

出　　处：《数学年刊（A辑）》2021年第2期179-188,共10页Chinese Annals of Mathematics

摘　　要：Pr表示最多r个素因子的正整数.作者证明了,对于任一足够大的实数N和1<C<CO,不等式|p^(c)+p^(c)_(r)-N|<N9/10(1-c/c)对素数p和Pr是可解的.特别地,当1<c<co=1.03074432…,有r=6这个结果改进了翟文广和曹晓东的结果.Let Pr denote an almost-prime with at most r prime factors,counted according to multiplicity.In this paper it is proved that for any sufficiently large real number N and 1<c<c0,the inequality|p^(c)+p^(c)_(r)-N|<N9/10(1-c/c)is solvable in a prime p and an almost-prime Pr.In particular for 1<c<c0=1.03074432……,the authors have r=6.This result constitutes an improvement upon that of W.G.Zhai and X.D.Cao.

关 键 词：丢番图不等式 指数和 殆素数 

分 类 号：O156.4[理学—数学]