{"title":"与调和数有关的几个同余","authors":"","doi":"10.52280/pujm.2021.530801","DOIUrl":null,"url":null,"abstract":"Let p be a prime greater than or equal to 5. In this paper, by using the harmonic numbers and Fermat quotient we establish congruences\ninvolving the sums\np−1 X2\nk=1\nµ\nk\nr\n¶\nHk,\np−1 X2\nk=1\n¡\n2k\nk\n¢2\n16k H\n(2)\nk\nand\np−1 X2\nk=1\n1\n4\nk\nµ\n2k\nk\n¶\nH\n(3)\nk\n.\nFor example,\np−1 X2\nk=0\n¡\n2k\nk\n¢2\n16k H\n(2)\nk ≡ 4E2p−4 − 8Ep−3\n¡\nmod p\n2\n¢\n,\nwhere H\n(m)\nk\nare the generalized harmonic numbers of order m and En are\nEuler numbers","PeriodicalId":205373,"journal":{"name":"Punjab University Journal of Mathematics","volume":"50 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Several Congruences Related to Harmonic Numbers\",\"authors\":\"\",\"doi\":\"10.52280/pujm.2021.530801\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let p be a prime greater than or equal to 5. In this paper, by using the harmonic numbers and Fermat quotient we establish congruences\\ninvolving the sums\\np−1 X2\\nk=1\\nµ\\nk\\nr\\n¶\\nHk,\\np−1 X2\\nk=1\\n¡\\n2k\\nk\\n¢2\\n16k H\\n(2)\\nk\\nand\\np−1 X2\\nk=1\\n1\\n4\\nk\\nµ\\n2k\\nk\\n¶\\nH\\n(3)\\nk\\n.\\nFor example,\\np−1 X2\\nk=0\\n¡\\n2k\\nk\\n¢2\\n16k H\\n(2)\\nk ≡ 4E2p−4 − 8Ep−3\\n¡\\nmod p\\n2\\n¢\\n,\\nwhere H\\n(m)\\nk\\nare the generalized harmonic numbers of order m and En are\\nEuler numbers\",\"PeriodicalId\":205373,\"journal\":{\"name\":\"Punjab University Journal of Mathematics\",\"volume\":\"50 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-08-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Punjab University Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.52280/pujm.2021.530801\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Punjab University Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52280/pujm.2021.530801","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let p be a prime greater than or equal to 5. In this paper, by using the harmonic numbers and Fermat quotient we establish congruences
involving the sums
p−1 X2
k=1
µ
k
r
¶
Hk,
p−1 X2
k=1
¡
2k
k
¢2
16k H
(2)
k
and
p−1 X2
k=1
1
4
k
µ
2k
k
¶
H
(3)
k
.
For example,
p−1 X2
k=0
¡
2k
k
¢2
16k H
(2)
k ≡ 4E2p−4 − 8Ep−3
¡
mod p
2
¢
,
where H
(m)
k
are the generalized harmonic numbers of order m and En are
Euler numbers
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
