«Previous Article|Table of Contents|Next Article»

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:

2018年04期

Page:

26-

Research Field:

·数学与计算机科学·

Publishing date:

Info

Title:

Note on the Weakly Prime-Additive Numbers

Author(s):

Fang Jinhui

School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China

Keywords:

weakly prime-additive numbers; Dirichlet’s theorem; Chinese remainder theorem

PACS:

O156.1

DOI:

10.3969/j.issn.1001-4616.2018.04.005

Abstract:

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=pα11+pα22+…+pαtt. 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=pα11+pα22+…+pα4t4t+pα4t+14t+1,where p1,p2,…,p4t+1 are distinct prime divisors of n and α1,α2,…,α4t+1 are positive integers.