{"title":"EXISTENCE OF EVEN PERFECT POLYNOMIALS","authors":"L. Gallardo, O. Rahavandrainy","doi":"10.59277/mrar.2023.25.75.1.47","DOIUrl":null,"url":null,"abstract":"\"Perfect polynomials are a natural analogue (in the ring Fp[x]) of multiperfect numbers (in the ring of integers). The latter numbers are classical objects that are poorly understood, since only their definition is simple. We describe, by elementary methods, the most basic objects in the polynomial case of the general problem. We display, for every prime number p ̸≡ 1mod 12 (resp. p ̸≡ 1mod 24) many new even non-splitting perfect (resp. unitary perfect) polynomials over Fp. Moreover, for any prime number p ̸≡ 1mod 24, new bi-unitary perfect polynomials are also given. These examples substantially improve our knowledge about these kinds of polynomials.\"","PeriodicalId":49858,"journal":{"name":"Mathematical Reports","volume":"147 6 1","pages":""},"PeriodicalIF":0.2000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Reports","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.59277/mrar.2023.25.75.1.47","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
"Perfect polynomials are a natural analogue (in the ring Fp[x]) of multiperfect numbers (in the ring of integers). The latter numbers are classical objects that are poorly understood, since only their definition is simple. We describe, by elementary methods, the most basic objects in the polynomial case of the general problem. We display, for every prime number p ̸≡ 1mod 12 (resp. p ̸≡ 1mod 24) many new even non-splitting perfect (resp. unitary perfect) polynomials over Fp. Moreover, for any prime number p ̸≡ 1mod 24, new bi-unitary perfect polynomials are also given. These examples substantially improve our knowledge about these kinds of polynomials."
期刊介绍：
The journal MATHEMATICAL REPORTS (formerly STUDII SI CERCETARI MATEMATICE) was founded in 1948 by the Mathematics Section of the Romanian Academy. It appeared under its first name until 1998 and received the name of Mathematical Reports in 1999. It is now published in one volume a year, consisting in 4 issues. The current average total number of pages is 500.
Our journal MATHEMATICAL REPORTS publishes original mathematical papers, written in English. Excellent survey articles may be also accepted. The editors will put strong emphasis on originality, quality and applicability.
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