{"title":"关于勒让德多项式模p^2的同余","authors":"Aeran Kim","doi":"10.46298/cm.10767","DOIUrl":null,"url":null,"abstract":"In this article, we extend Z. H. Sun's congruences concerning Legendre polynomials P p−1 2 (x) to P p+1 2 (x) for odd prime p, which enables us to deduce some congruences resembling p+1 2 ∑ k=0 4pk + 4k 2 − 1 16 k (2k − 1) 2 (2k k)2 (mod p 2).\n 이 논문에서 우리는 Z. H. Sun의 르장드르 다항식의 합동식 P p−1 2 (x) 에서 P p+1 2 (x) (단, p는 소수) 까지를 이용해서 이 합동식과 비슷한 합동식 p+1 2 ∑ k=0 4pk + 4k 2 − 1 16 k (2k − 1) 2 (2k k)2 (mod p 2) 을 유도한다.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"CONGRUENCES CONCERNING LEGENDRE POLYNOMIALS MODULO p^2\",\"authors\":\"Aeran Kim\",\"doi\":\"10.46298/cm.10767\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we extend Z. H. Sun's congruences concerning Legendre polynomials P p−1 2 (x) to P p+1 2 (x) for odd prime p, which enables us to deduce some congruences resembling p+1 2 ∑ k=0 4pk + 4k 2 − 1 16 k (2k − 1) 2 (2k k)2 (mod p 2).\\n 이 논문에서 우리는 Z. H. Sun의 르장드르 다항식의 합동식 P p−1 2 (x) 에서 P p+1 2 (x) (단, p는 소수) 까지를 이용해서 이 합동식과 비슷한 합동식 p+1 2 ∑ k=0 4pk + 4k 2 − 1 16 k (2k − 1) 2 (2k k)2 (mod p 2) 을 유도한다.\",\"PeriodicalId\":37836,\"journal\":{\"name\":\"Communications in Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-02-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/cm.10767\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/cm.10767","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
In this article, we extend Z. H. Sun's congruences concerning Legendre polynomials P P - 1 2 (x) to P P +1 2 (x) for odd prime P;which enables us to deduce some congruences resembling p + 1 2∑k = 0 4pk 16 k (2k + 4k 2 - 1, - 1) 2 (2k k) 2 (mod p 2)。这篇论文中,我们z·h·sun的章吱扭다항식的联合式p 2 (x)在p - 1, p = p + 1 2 (x)段,p是质数)到利用类似联合式的联合式p + 1 2∑k = 0 4pk 16 k (2k + 4k 2 - 1, - 1) 2 (2k k) 2 (mod p 2)诱导的。
In this article, we extend Z. H. Sun's congruences concerning Legendre polynomials P p−1 2 (x) to P p+1 2 (x) for odd prime p, which enables us to deduce some congruences resembling p+1 2 ∑ k=0 4pk + 4k 2 − 1 16 k (2k − 1) 2 (2k k)2 (mod p 2).
이 논문에서 우리는 Z. H. Sun의 르장드르 다항식의 합동식 P p−1 2 (x) 에서 P p+1 2 (x) (단, p는 소수) 까지를 이용해서 이 합동식과 비슷한 합동식 p+1 2 ∑ k=0 4pk + 4k 2 − 1 16 k (2k − 1) 2 (2k k)2 (mod p 2) 을 유도한다.
期刊介绍：
Communications in Mathematics publishes research and survey papers in all areas of pure and applied mathematics. To be acceptable for publication, the paper must be significant, original and correct. High quality review papers of interest to a wide range of scientists in mathematics and its applications are equally welcome.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
