{"title":"短间隔内三个对素数整数的乘积","authors":"A. Islam","doi":"10.1112/S1461157012000058","DOIUrl":null,"url":null,"abstract":"The existence of products of three pairwise coprime integers is investigated in short intervals of the form (x, x + x 1 2 ]. A general theorem is proved which shows that such integer products exist provided there is a bound on the product of any two of them. A particular case of relevance to elliptic curve cryptography, where all three integers are of order x 1 3 , is presented as a corollary to this result.","PeriodicalId":54381,"journal":{"name":"Lms Journal of Computation and Mathematics","volume":"15 1","pages":"59-70"},"PeriodicalIF":0.0000,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1112/S1461157012000058","citationCount":"3","resultStr":"{\"title\":\"Products of three pairwise coprime integers in short intervals\",\"authors\":\"A. Islam\",\"doi\":\"10.1112/S1461157012000058\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The existence of products of three pairwise coprime integers is investigated in short intervals of the form (x, x + x 1 2 ]. A general theorem is proved which shows that such integer products exist provided there is a bound on the product of any two of them. A particular case of relevance to elliptic curve cryptography, where all three integers are of order x 1 3 , is presented as a corollary to this result.\",\"PeriodicalId\":54381,\"journal\":{\"name\":\"Lms Journal of Computation and Mathematics\",\"volume\":\"15 1\",\"pages\":\"59-70\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1112/S1461157012000058\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lms Journal of Computation and Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1112/S1461157012000058\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lms Journal of Computation and Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1112/S1461157012000058","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 3
摘要
在(x, x + x 12]的短区间内研究了三个对素数整数积的存在性。证明了一个一般定理，证明了只要任意两个整数积有一个界，就存在这样的整数积。与椭圆曲线密码学相关的一个特殊情况，其中所有三个整数都是x 1 3阶，作为该结果的推论。
Products of three pairwise coprime integers in short intervals
The existence of products of three pairwise coprime integers is investigated in short intervals of the form (x, x + x 1 2 ]. A general theorem is proved which shows that such integer products exist provided there is a bound on the product of any two of them. A particular case of relevance to elliptic curve cryptography, where all three integers are of order x 1 3 , is presented as a corollary to this result.
期刊介绍：
LMS Journal of Computation and Mathematics has ceased publication. Its final volume is Volume 20 (2017). LMS Journal of Computation and Mathematics is an electronic-only resource that comprises papers on the computational aspects of mathematics, mathematical aspects of computation, and papers in mathematics which benefit from having been published electronically. The journal is refereed to the same high standard as the established LMS journals, and carries a commitment from the LMS to keep it archived into the indefinite future. Access is free until further notice.
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