Pub Date : 2021-11-24DOI: 10.1201/9781003275947-10
S. Kundu, Sypriyo Mazumder
{"title":"Integers of Special Forms","authors":"S. Kundu, Sypriyo Mazumder","doi":"10.1201/9781003275947-10","DOIUrl":"https://doi.org/10.1201/9781003275947-10","url":null,"abstract":"","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134440080","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}
{"title":"Prerequisites","authors":"S. Kundu, Sypriyo Mazumder","doi":"10.1201/9781003275947-1","DOIUrl":"https://doi.org/10.1201/9781003275947-1","url":null,"abstract":"","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129807101","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}
{"title":"Theory of Quadratic Residues","authors":"S. Kundu, Sypriyo Mazumder","doi":"10.1201/9781003275947-9","DOIUrl":"https://doi.org/10.1201/9781003275947-9","url":null,"abstract":"","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129841275","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}
Pub Date : 2021-11-24DOI: 10.1201/9781003275947-13
S. Kundu, Sypriyo Mazumder
{"title":"Integers as Sums of Squares","authors":"S. Kundu, Sypriyo Mazumder","doi":"10.1201/9781003275947-13","DOIUrl":"https://doi.org/10.1201/9781003275947-13","url":null,"abstract":"","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117167044","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}
Pub Date : 2021-11-24DOI: 10.1201/9781003275947-11
S. Kundu, Sypriyo Mazumder
{"title":"Continued Fractions","authors":"S. Kundu, Sypriyo Mazumder","doi":"10.1201/9781003275947-11","DOIUrl":"https://doi.org/10.1201/9781003275947-11","url":null,"abstract":"","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"215 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114596833","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}
Let p be a prime and let a ∈ Z + be such that a is not a multiple of p, i.e., p does not divide a. Let's look at the set Z p of congruence classes modulo p. There are exactly p congruence classes and We define the function f a : Z p → Z p by f a ([x] p) = [ax] p .
设p是素数，且a∈Z +使得a不是p的倍数，即p不能除a。我们来看同余类的集合zp对p取模，有p个同余类，我们定义函数f a: zp→zp by f a ([x] p) = [ax] p。
{"title":"Fermat's Little Theorem","authors":"S. Kundu, Sypriyo Mazumder","doi":"10.3840/000970","DOIUrl":"https://doi.org/10.3840/000970","url":null,"abstract":"Let p be a prime and let a ∈ Z + be such that a is not a multiple of p, i.e., p does not divide a. Let's look at the set Z p of congruence classes modulo p. There are exactly p congruence classes and We define the function f a : Z p → Z p by f a ([x] p) = [ax] p .","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127922831","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}
Pub Date : 2021-11-24DOI: 10.1201/9781003275947-12
S. Kundu, Sypriyo Mazumder
{"title":"Few Non-Linear Diophantine Equations","authors":"S. Kundu, Sypriyo Mazumder","doi":"10.1201/9781003275947-12","DOIUrl":"https://doi.org/10.1201/9781003275947-12","url":null,"abstract":"","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115542474","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}
Pub Date : 2021-11-24DOI: 10.1007/978-0-387-72350-1_1
S. Kundu, Sypriyo Mazumder
{"title":"Arithmetic Functions","authors":"S. Kundu, Sypriyo Mazumder","doi":"10.1007/978-0-387-72350-1_1","DOIUrl":"https://doi.org/10.1007/978-0-387-72350-1_1","url":null,"abstract":"","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128087489","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}
Pub Date : 2021-11-24DOI: 10.1016/s0079-8169(08)61694-3
S. Kundu, Sypriyo Mazumder
{"title":"Theory of Divisibility","authors":"S. Kundu, Sypriyo Mazumder","doi":"10.1016/s0079-8169(08)61694-3","DOIUrl":"https://doi.org/10.1016/s0079-8169(08)61694-3","url":null,"abstract":"","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121156196","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}
{"title":"Theory of Congruences","authors":"S. Kundu, Sypriyo Mazumder","doi":"10.1201/9781003275947-4","DOIUrl":"https://doi.org/10.1201/9781003275947-4","url":null,"abstract":"","PeriodicalId":280679,"journal":{"name":"Number Theory and its Applications","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127997600","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}
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