Zobrazeno 1 - 10 of 23 pro vyhledávání: '"ZAFER ŞİAR"'
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Akademický článek
On perfect powers in $k$-generalized Pell sequence
Autor: Zafer Şiar, Refik Keskin, Elif Segah Öztaş
Publikováno v: Mathematica Bohemica, Vol 148, Iss 4, Pp 507-518 (2023)
Let $k\geq2$ and let $(P_n^{(k)})_{n\geq2-k}$ be the $k$-generalized Pell sequence defined by \begin{equation*} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)} \end{equation*}for $n\geq2$ with initial conditions \begin{equation*} P_{-(k-2
Externí odkaz: https://doaj.org/article/34e113f1b2354c8ab290f8e9584e4041
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3
On the exponential Diophantine equation Fnx ± Fmx = a with a ∈{Fr,Lr}
Autor: Zafer Şiar
Publikováno v: International Journal of Number Theory. 19:41-57
In this paper, we will answer the question of when the sum or the difference of [Formula: see text]th powers of any two Fibonacci numbers becomes a Fibonacci number or a Lucas number. We prove that if this is possible with [Formula: see text], then [
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a63bd7e1f3b25cc35fc335c58b2d6189
https://doi.org/10.1142/s1793042123500021
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6
Repdigits base b as products of two Fibonacci numbers
Autor: Zafer Şiar, Refik Keskin, Fatih Erduvan
Publikováno v: Indian Journal of Pure and Applied Mathematics. 52:861-868
Let $$(F_{n})$$ be the sequence of Fibonacci numbers defined by $$F_{0}=0,~F_{1}=1$$ , and $$F_{n}=F_{n-1}+F_{n-2}$$ for $$n\ge 2.$$ Let $$2\le m\le n$$ and $$b=2,3,4,5,6,7,8,9.$$ In this study, we show that if $$F_{m}F_{n}$$ is a repdigit in base b
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d9ccc463f239105fb7d4277fe60c704c
https://doi.org/10.1007/s13226-021-00041-8
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7
Fibonacci or Lucas Numbers Which are Products of Two Repdigits in Base b
Autor: Fatih Erduvan, Zafer Şiar, Refik Keskin
Publikováno v: Bulletin of the Brazilian Mathematical Society, New Series. 52:1025-1040
In this study, we find all Fibonacci and Lucas numbers which can be expressible as a product of two repdigits in the base b. It is shown that the largest Fibonacci and Lucas numbers which can be expressible as a product of two repdigits are $$F_{12}=
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a4a3d3712d8697003f97410ad0c3d249
https://doi.org/10.1007/s00574-021-00243-y
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8
On the Diophantine equation $F_{n}-F_{m}=2^{a}$
Autor: Zafer Şiar, Refik Keskin
Publikováno v: Colloquium Mathematicum. 159:119-126
In this paper, we solve Diophantine equation in the tittle in nonnegative integers m,n, and a. In order to prove our result, we use lower bounds for linear forms in logarithms and and a version of the Baker-Davenport reduction method in diophantine a
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::936243ce02924247738c7f352a6ee5e5
https://doi.org/10.4064/cm7485-12-2018
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10
Repdigits base b as products of two Lucas numbers
Autor: Zafer Şiar, Fatih Erduvan, Refik Keskin
Publikováno v: Quaestiones Mathematicae; Vol. 44 No. 10 (2021); 1283-1293
Let (Ln ) be the sequence of Lucas numbers defined by L 0 = 2, L 1 = 1, and Ln = L n−1 + L n−2 for n ≥ 2. Let 0 ≤ m ≤ n and b = 2, 3, 4, 5, 6, 7, 8, 9. In this study, we show that if LmLn is a repd...
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6aba251098d35c814230729319d30de9
https://www.ajol.info/index.php/qm/article/view/218464
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