Strong Goldbach Conjecture and Generalized Moser-Type Inequalities

作     者：ZHANG Shaohua ZHANG Shaohua

作者机构：School of Mathematics and StatisticsYangtze Normal UniversityChongqing 408102China 

出 版 物：《Wuhan University Journal of Natural Sciences》 (武汉大学学报（自然科学英文版）)

年 卷 期：2021年第26卷第1期

页      面：15-18页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：the National Natural Science Foundation of China(11401050) Scientific Research Innovation Team Project Affiliated to Yangtze Normal University(2016XJTD01) 

主　　题：Strong Goldbach Conjecture pairwise coprime Euler totient function prime-counting function 

摘      要：In this paper,we consider the generalized Moser-type inequalities,sayφ(n)≥kπ(n),where k is an integer greater than 1,φ(n)is Euler function andπ(n)is the prime counting *** computer,Pierre Dusart’s inequality onπ(n)and Rosser-Schoenfeld’s inequality involvingφ(n),we give all solutions ofφ(n)=2π(n)andφ(n)=3π(n),***,we obtain the best lower bound that Moser-type inequalitiesφ(n)kπ(n)hold for k=2,*** consequences,we show that every even integer greater than 210 is the sum of two coprime composite,every odd integer greater than 175 is the sum of three pairwise coprime odd composite numbers,and every odd integer greater than 53 can be represented as p+x+y,where p is prime,x and y are composite numbers satisfying that p,and x and y are pairwise ***,we give a new equivalent form of Strong Goldbach Conjecture.