{"title":"一个丢番图方程，包括斐波那契系数和斐波那契系数","authors":"Nurettin IRMAK","doi":"10.31801/cfsuasmas.1247415","DOIUrl":null,"url":null,"abstract":"In this paper, we solve the equation \\begin{equation*} \\sum_{k=0}^{m} {{2m+1}\\brack{k}}_{F}\\pm F_{t}=F_{n}, \\end{equation*}% under weak assumptions. Here, $F_n$ is $n^{th}$ Fibonacci number and ${{.}\\brack {.}}_{F}$ denotes Fibonomial coefficient.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":"23 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Diophantine equation including Fibonacci and Fibonomial coefficients\",\"authors\":\"Nurettin IRMAK\",\"doi\":\"10.31801/cfsuasmas.1247415\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we solve the equation \\\\begin{equation*} \\\\sum_{k=0}^{m} {{2m+1}\\\\brack{k}}_{F}\\\\pm F_{t}=F_{n}, \\\\end{equation*}% under weak assumptions. Here, $F_n$ is $n^{th}$ Fibonacci number and ${{.}\\\\brack {.}}_{F}$ denotes Fibonomial coefficient.\",\"PeriodicalId\":44692,\"journal\":{\"name\":\"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31801/cfsuasmas.1247415\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31801/cfsuasmas.1247415","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文对该方程进行了求解 \begin{equation*} \sum_{k=0}^{m} {{2m+1}\brack{k}}_{F}\pm F_{t}=F_{n}, \end{equation*}% under weak assumptions. Here, $F_n$ is $n^{th}$ Fibonacci number and ${{.}\brack {.}}_{F}$ denotes Fibonomial coefficient.
A Diophantine equation including Fibonacci and Fibonomial coefficients
In this paper, we solve the equation \begin{equation*} \sum_{k=0}^{m} {{2m+1}\brack{k}}_{F}\pm F_{t}=F_{n}, \end{equation*}% under weak assumptions. Here, $F_n$ is $n^{th}$ Fibonacci number and ${{.}\brack {.}}_{F}$ denotes Fibonomial coefficient.
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