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Infinitely many composites 无限多的复合材料
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.4
Nick Lord, Des MacHale
{"title":"Infinitely many composites","authors":"Nick Lord, Des MacHale","doi":"10.1017/mag.2024.4","DOIUrl":"https://doi.org/10.1017/mag.2024.4","url":null,"abstract":"In number theory, we frequently ask if there are infinitely many prime numbers of a certain type. For example, if n is a natural number:\u0000(i)Are there infinitely many (Mersenne) primes of the form 2n − 1?(ii)Are there infinitely many primes of the form n2 + 1?These problems are often very difficult and many remain unsolved to this day, despite the efforts of many great mathematicians. However, we can sometimes comfort ourselves by asking if there are infinitely many composite numbers of a certain type. These questions are often (but not always) easier to answer. For example, echoing (i) above, we can ask if there are infinitely many composites of the form 2p − 1 with p a prime number but (to the best of our knowledge) this remains an unsolved problem. Of course, it must be the case that there are either infinitely many primes or infinitely many composites of the form 2p − 1 and it seems strange that we currently cannot decide on either of them.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139836048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Singular matrices and pairwise-tangent circles 奇异矩阵和对切圆
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.3
A. Beardon
{"title":"Singular matrices and pairwise-tangent circles","authors":"A. Beardon","doi":"10.1017/mag.2024.3","DOIUrl":"https://doi.org/10.1017/mag.2024.3","url":null,"abstract":"The idea of using the generalised inverse of a singular matrix A to solve the matrix equation Ax = b has been discussed in the earlier papers [1, 2, 3, 4] in the Gazette. Here we discuss three simple geometric questions which are of interest in their own right, and which illustrate the use of the generalised inverse of a matrix. The three questions are about polygons and circles in the Euclidean plane. We need not assume that a polygon is a simple closed curve, nor that it is convex: indeed, abstractly, a polygon is just a finite sequence (v1, …, vn) of its distinct, consecutive, vertices. It is convenient to let vn + 1 = v1 and (later) Cn + 1 = C1.","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139836359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
108.11 Euler’s limit—revisited 108.11 欧拉极限重温
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.28
Bikash Chakraborty, Sagar Chakraborty
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引用次数: 0
108.12 Proof without words: a lower bound for n! 108.12 无字证明：n 的下限！
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.29
Mehdi Hassani
{"title":"108.12 Proof without words: a lower bound for n!","authors":"Mehdi Hassani","doi":"10.1017/mag.2024.29","DOIUrl":"https://doi.org/10.1017/mag.2024.29","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
MAG volume 108 issue 571 Cover and Front matter 博物周刊》第 108 卷第 571 期封面和封底
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.1
{"title":"MAG volume 108 issue 571 Cover and Front matter","authors":"","doi":"10.1017/mag.2024.1","DOIUrl":"https://doi.org/10.1017/mag.2024.1","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Theory of infinite sequences and series by Ludmila Bourchtein and Andrei Bourchtein , pp. 377, £54.99, (paper), ISBN 978-3-03079-430-9, Springer Verlag (2022) 无穷序列和数列理论》，Ludmila Bourchtein 和 Andrei Bourchtein 著，第 377 页，54.99 英镑（纸质版），ISBN 978-3-03079-430-9, Springer Verlag (2022)
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.48
Martin Lukarevski
{"title":"Theory of infinite sequences and series by Ludmila Bourchtein and Andrei Bourchtein , pp. 377, £54.99, (paper), ISBN 978-3-03079-430-9, Springer Verlag (2022)","authors":"Martin Lukarevski","doi":"10.1017/mag.2024.48","DOIUrl":"https://doi.org/10.1017/mag.2024.48","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The one true logic: a monist manifesto, by Owen Griffiths and A. C. Paseau, pp 232, ISBN 978-0-19-882971-3, Oxford University Press (2022). 唯一真实的逻辑：一元论宣言》，欧文-格里菲斯和 A. C. 帕索著，第 232 页，国际标准书号 978-0-19-882971-3，牛津大学出版社（2022 年）。
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.51
Alan Slomson
{"title":"The one true logic: a monist manifesto, by Owen Griffiths and A. C. Paseau, pp 232, ISBN 978-0-19-882971-3, Oxford University Press (2022).","authors":"Alan Slomson","doi":"10.1017/mag.2024.51","DOIUrl":"https://doi.org/10.1017/mag.2024.51","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A student's guide to Laplace transforms by Daniel Fleisch , pp. 218, £17.99, (paper), ISBN 978-1-00909-629-4, Cambridge University Press (2022) 拉普拉斯变换学生指南》，丹尼尔-弗莱施著，第 218 页，17.99 英镑（纸质），ISBN 978-1-00909-629-4，剑桥大学出版社（2022 年）。
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.49
Sue Colwell
{"title":"A student's guide to Laplace transforms by Daniel Fleisch , pp. 218, £17.99, (paper), ISBN 978-1-00909-629-4, Cambridge University Press (2022)","authors":"Sue Colwell","doi":"10.1017/mag.2024.49","DOIUrl":"https://doi.org/10.1017/mag.2024.49","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139836354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
108.13 Indeterminate exponentials without tears 108.13 无泪不定指数
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.30
Reza Farhadian, Vadim Ponomarenko
{"title":"108.13 Indeterminate exponentials without tears","authors":"Reza Farhadian, Vadim Ponomarenko","doi":"10.1017/mag.2024.30","DOIUrl":"https://doi.org/10.1017/mag.2024.30","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139774927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
108.07 De Moivre’s theorem via difference equations 108.07 通过差分方程的德莫伊弗定理
The Mathematical Gazette Pub Date : 2024-02-15 DOI: 10.1017/mag.2024.24
T. N. Lucas
{"title":"108.07 De Moivre’s theorem via difference equations","authors":"T. N. Lucas","doi":"10.1017/mag.2024.24","DOIUrl":"https://doi.org/10.1017/mag.2024.24","url":null,"abstract":"","PeriodicalId":22812,"journal":{"name":"The Mathematical Gazette","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139775214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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