{"title":"Euler tangent numbers modulo 720 and Genocchi numbers modulo 45","authors":"A. Dzhumadil'daev, Medet Jumadildayev","doi":"10.3792/pjaa.98.012","DOIUrl":null,"url":null,"abstract":": We establish congruences for higher order Euler polynomials modulo 720. We apply this result for constructing analogues of Stern congruences for Euler secant numbers E 4 n (cid:3) 5 ð mod 60 Þ ; E 4 n þ 2 (cid:3) (cid:4) 1 ð mod 60 Þ to Euler tangent numbers and Genocchi numbers. We prove that Euler tangent numbers satisfy the following congruences E 4 n þ 1 (cid:3) 16 ð mod 720 Þ , and E 4 n þ 3 (cid:3) (cid:4) 272 ð mod 720 Þ . We establish 12-periodic property of Genocchi numbers modulo 45.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3792/pjaa.98.012","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 establish congruences for higher order Euler polynomials modulo 720. We apply this result for constructing analogues of Stern congruences for Euler secant numbers E 4 n (cid:3) 5 ð mod 60 Þ ; E 4 n þ 2 (cid:3) (cid:4) 1 ð mod 60 Þ to Euler tangent numbers and Genocchi numbers. We prove that Euler tangent numbers satisfy the following congruences E 4 n þ 1 (cid:3) 16 ð mod 720 Þ , and E 4 n þ 3 (cid:3) (cid:4) 272 ð mod 720 Þ . We establish 12-periodic property of Genocchi numbers modulo 45.