摘要
设n是正整数,若n有至少两个互异素因子,而且存在n的互异素因子p_1,p_2,…,pt和正整数α_1,α_2,…,αt使得n=p_1^(α1)+p_2^(2α)+…+p_t^(αt),那么我们称n为弱素性可加数.本文中,我们通过多次巧妙应用中国剩余定理、Dirichlet定理和二次互反律证明:对任意正整数m和t,存在无穷多个弱素性可加数n使得m|n且n=p_1^(α1)+p_2^(α2)+…+p_(4t)^(4αt)+p_(4t+1)^(αt4+1),其中p1,p2,…,p_(4t+1)是n的互异素因子,α_1,α_2,…,α_(4t+1)是正整数.
A positive integer n is called weakly prime-additive if n has at least two distinct prime divisors and there exist distinct prime divisors p1,p2,…,pt of n and positive integers α1,α2,…,αt such that n=p1^α1+p2^α2+…+pt^αt.In this paper,by employing Chinese remainder theorem,Dirichlet’s theorem and the quadratic reciprocity law,we prove that,for any positive integers m and t,there exist infinitely many weakly prime-additive numbers n with m|n and n=p1^α1+p2^α2+…+p4t^α4t+p4t+1^α4t+1,where p1,p2,…,p4t+1 are distinct prime divisors of n and α1,α2,…,α4t+1 are positive integers.
作者
方金辉
Fang Jinhui(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)
出处
《南京师大学报（自然科学版）》
CAS
CSCD
北大核心
2018年第4期26-28,共3页
Journal of Nanjing Normal University(Natural Science Edition)
基金
国家自然科学基金(11671211)
