与Komornik多项式相连的丢番图方程

Pub Date : 2020-06-12 DOI:10.3336/gm.55.1.02

A. Bazsó, A. Bérczes, Ondřej Kolouch, I. Pink, J. Šustek

{"title":"与Komornik多项式相连的丢番图方程","authors":"A. Bazsó, A. Bérczes, Ondřej Kolouch, I. Pink, J. Šustek","doi":"10.3336/gm.55.1.02","DOIUrl":null,"url":null,"abstract":"We investigate the power and polynomial values of the polynomials Pn(X) = ∏ n k=0 ( X2·3 k − X3 k − 1 ) for n ∈ N. We prove various ineffective and effective finiteness results. In the case 0 ≤ n ≤ 3, we determine all pairs x, y of integers such that Pn(x) = y2 or Pn(x) = y3.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Diophantine equations connected to the Komornik polynomials\",\"authors\":\"A. Bazsó, A. Bérczes, Ondřej Kolouch, I. Pink, J. Šustek\",\"doi\":\"10.3336/gm.55.1.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate the power and polynomial values of the polynomials Pn(X) = ∏ n k=0 ( X2·3 k − X3 k − 1 ) for n ∈ N. We prove various ineffective and effective finiteness results. In the case 0 ≤ n ≤ 3, we determine all pairs x, y of integers such that Pn(x) = y2 or Pn(x) = y3.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-06-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3336/gm.55.1.02\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3336/gm.55.1.02","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

我们研究了n∈n时多项式Pn(X) =∏n k=0 (X2·3k−X3 k−1)的幂次和多项式值。我们证明了各种无效和有效的有限性结果。在0≤n≤3的情况下，我们确定所有的整数对x, y使Pn(x) = y2或Pn(x) = y3。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Diophantine equations connected to the Komornik polynomials

We investigate the power and polynomial values of the polynomials Pn(X) = ∏ n k=0 ( X2·3 k − X3 k − 1 ) for n ∈ N. We prove various ineffective and effective finiteness results. In the case 0 ≤ n ≤ 3, we determine all pairs x, y of integers such that Pn(x) = y2 or Pn(x) = y3.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助