REFIK KESKIN
Articles written in Proceedings – Mathematical Sciences
Volume 124 Issue 3 August 2014 pp 301-313
Positive Integer Solutions of the Diophantine Equation $x^2 - L_n xy + (-1)^n y^2 = \pm 5^r$
In this paper, we consider the equation $x^2-L_n xy+(-1)^n y^2=\pm 5^r$ and determine the values of 𝑛 for which the equation has positive integer solutions 𝑥 and 𝑦. Moreover, we give all positive integer solutions of the equation $x^2-L_n xy+(-1)^n y^2=\pm 5^r$ when the equation has positive integer solutions.
Volume 129 Issue 5 November 2019 Article ID 0069 Research Article
A note on the exponential diophantine equation $(a^{n} − 1)(b^{n} − 1) = x^{2}$
In 2002, Luca and Walsh (
Volume 129 Issue 5 November 2019 Article ID 0081 Research Article
On solutions of the diophantine equation $F_{n} − F_{m} = 3^{a}$
BAHAR DEMIRTÜRK BITIM REFIK KESKIN
In this paper, we find non-negative ($n, m, a$) integer solutions of thediophantine equation $F_{n} − F_{m} = 3^{a}$, where $Fn$ and $Fm$ are Fibonacci numbers. For proving our theorem, we use lower bounds in linear forms.
Volume 130 All articles Published: 15 March 2020 Article ID 0028 Research Article
Repdigits as products of two Fibonacci or Lucas numbers
In this study, we show that if $2 \leq m \leq n$ and $F_{m} F_{n}$ represents a repdigit, then $(m, n)$ belongs to the set $$\{(2, 2), (2, 3), (3, 3), (2, 4), (3, 4), (4, 4), (2, 5), (2, 6), (2, 10)\}.$$ Also, we show that if $0 \leq m \leq n$ and $L_{m} L_{n}$ represents a repdigit, then $(m, n)$ belongs to the set $$\left\{ \begin{array}{l}(0, 0), (0, 1), (1, 1), (0, 2), (1, 2), (2, 2), (0, 3),\\ (1, 3), (1, 4), (1, 5), (2, 5), (3, 5), (4, 5) \end{array}\right\}$$
Volume 130, 2020
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