{"title":"四个偶数的相等和","authors":"Kimtai Boaz Simatwo","doi":"10.9734/arjom/2024/v20i5802","DOIUrl":null,"url":null,"abstract":"Let u, v, w, z, k, m and I be any integers such that k = z - w = w - v = v - u . The study of integer I for which I = u2n + v2n + w2n + z2n = k2 + m2 + r2 is not known. This study is therefore, set to partially overcome this challenge by introducing new formula relating sums of four even powers as an exact sum of three squares.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"54 s186","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Equal Sums of Four Even Powers\",\"authors\":\"Kimtai Boaz Simatwo\",\"doi\":\"10.9734/arjom/2024/v20i5802\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let u, v, w, z, k, m and I be any integers such that k = z - w = w - v = v - u . The study of integer I for which I = u2n + v2n + w2n + z2n = k2 + m2 + r2 is not known. This study is therefore, set to partially overcome this challenge by introducing new formula relating sums of four even powers as an exact sum of three squares.\",\"PeriodicalId\":281529,\"journal\":{\"name\":\"Asian Research Journal of Mathematics\",\"volume\":\"54 s186\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asian Research Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.9734/arjom/2024/v20i5802\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Research Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.9734/arjom/2024/v20i5802","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
设 u、v、w、z、k、m 和 I 是任意整数，使得 k = z - w = w - v = v - u 。关于 I = u2n + v2n + w2n + z2n = k2 + m2 + r2 的整数 I 的研究尚不清楚。因此，本研究通过引入有关四个偶数幂的和为三个平方的精确和的新公式来部分克服这一难题。
Let u, v, w, z, k, m and I be any integers such that k = z - w = w - v = v - u . The study of integer I for which I = u2n + v2n + w2n + z2n = k2 + m2 + r2 is not known. This study is therefore, set to partially overcome this challenge by introducing new formula relating sums of four even powers as an exact sum of three squares.
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