{"title":"k -广义Pell序列的完全幂","authors":"Z. Şiar, R. Keskin, Elif Segah Öztas","doi":"10.21136/mb.2022.0033-22","DOIUrl":null,"url":null,"abstract":". Let k > 2 and let ( P ( k ) n ) n > 2 − k be the k -generalized Pell sequence defined by P ( k ) n = 2 P ( k ) n − 1 + P ( k ) n − 2 + . . . + P ( k ) n − k for n > 2 with initial conditions In this study, we handle the equation P ( k ) n = y m in positive integers n , m , y , k such that k, y > 2 , and give an upper bound on n. Also, we will show that the equation P ( k ) n = y m with 2 6 y 6 1000 has only one solution given by P (2)7 = 13 2 .","PeriodicalId":45392,"journal":{"name":"Mathematica Bohemica","volume":" ","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On perfect powers in $k$-generalized Pell sequence\",\"authors\":\"Z. Şiar, R. Keskin, Elif Segah Öztas\",\"doi\":\"10.21136/mb.2022.0033-22\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Let k > 2 and let ( P ( k ) n ) n > 2 − k be the k -generalized Pell sequence defined by P ( k ) n = 2 P ( k ) n − 1 + P ( k ) n − 2 + . . . + P ( k ) n − k for n > 2 with initial conditions In this study, we handle the equation P ( k ) n = y m in positive integers n , m , y , k such that k, y > 2 , and give an upper bound on n. Also, we will show that the equation P ( k ) n = y m with 2 6 y 6 1000 has only one solution given by P (2)7 = 13 2 .\",\"PeriodicalId\":45392,\"journal\":{\"name\":\"Mathematica Bohemica\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-09-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematica Bohemica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21136/mb.2022.0033-22\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Bohemica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21136/mb.2022.0033-22","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
摘要
． 让k n > 2,让(P (k)) k n > 2−be the k -generalized佩尔奈德fi序列n: P (k) = 2 (k) n−1 P + P (k) n−2。。P (k) + n (n−k for > 2与初始条件在这个研究,我们把手the equation P (k) n = y在积极integers n, m、y y这样的那个k, k > 2,和给上束缚在一个n .也会,我们会show that the equation P (k) n = m和y = 2 6 y 1000唯一溶液赐予了:P(2) 7 = 13。
On perfect powers in $k$-generalized Pell sequence
. Let k > 2 and let ( P ( k ) n ) n > 2 − k be the k -generalized Pell sequence defined by P ( k ) n = 2 P ( k ) n − 1 + P ( k ) n − 2 + . . . + P ( k ) n − k for n > 2 with initial conditions In this study, we handle the equation P ( k ) n = y m in positive integers n , m , y , k such that k, y > 2 , and give an upper bound on n. Also, we will show that the equation P ( k ) n = y m with 2 6 y 6 1000 has only one solution given by P (2)7 = 13 2 .
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