{"title":"Elementary Formulas for Greatest Common Divisors and Semiprime Factors","authors":"Joseph M. Shunia","doi":"arxiv-2407.03357","DOIUrl":null,"url":null,"abstract":"We present new formulas for computing greatest common divisors (GCDs) and\nextracting the prime factors of semiprimes using only elementary arithmetic\noperations: addition, subtraction, multiplication, floored division, and\nexponentiation. Our GCD formula simplifies a result of Mazzanti, and is derived\nusing Kronecker substitution techniques from our previous work. We utilize the\nGCD formula, along with recent developments on arithmetic terms for square\nroots and factorials, to derive explicit expressions for the prime factors of a\nsemiprime $n=pq$.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"156 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - General Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.03357","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We present new formulas for computing greatest common divisors (GCDs) and
extracting the prime factors of semiprimes using only elementary arithmetic
operations: addition, subtraction, multiplication, floored division, and
exponentiation. Our GCD formula simplifies a result of Mazzanti, and is derived
using Kronecker substitution techniques from our previous work. We utilize the
GCD formula, along with recent developments on arithmetic terms for square
roots and factorials, to derive explicit expressions for the prime factors of a
semiprime $n=pq$.
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