On integers not of the form ±𝑝^{𝑎}±𝑞^{𝑏}

Author:

Sun Zhi-Wei

Abstract

In 1975 F. Cohen and J.L. Selfridge found a 94-digit positive integer which cannot be written as the sum or difference of two prime powers. Following their basic construction and introducing a new method to avoid a bunch of extra congruences, we are able to prove that if x 47867742232066880047611079 ( mod 66483034025018711639862527490 ) , \begin{equation*} \hspace {-1.5pc} x\equiv 47867742232066880047611079 (\operatorname {mod} 66483034025018711639862527490), \hspace {-1.5pc} \end{equation*} then x x is not of the form ± p a ± q b \pm p^{a}\pm q^{b} where p , q p,q are primes and a , b a,b are nonnegative integers.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference15 articles.

1. [BV] G.D. Birkhoff and H.S. Vandiver, On the integral divisors of 𝑎ⁿ-𝑏ⁿ, Ann. Math. 5 (1904), 173–180.

2. Not every number is the sum or difference of two prime powers;Cohen, Fred;Math. Comp.,1975

3. The lattice theory of ova;Ward, Morgan;Ann. of Math. (2),1939

4. On the sum of a prime and of two powers of two;Crocker, Roger;Pacific J. Math.,1971

5. Annihilator ideals and representation iteration for abstract rings;Everett, C. J., Jr.;Duke Math. J.,1939

Cited by 37 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. An exploration of Nathanson’s g-adic representations of integers;Involve, a Journal of Mathematics;2022-12-31

2. Twin-prime and Goldbach theorems for Z[[x]];Journal of Number Theory;2020-08

3. A NOTE ON THE SUM OF RECIPROCALS;Bulletin of the Australian Mathematical Society;2019-05-17

4. Abstract Recursion and Intrinsic Complexity;2018-11-23

5. On integers not of the form Fn ± pa;International Journal of Number Theory;2016-02-18

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3