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math.NT2021
A Note on Terai's Conjecture Concerning the Exponential Diophantine Equation x^{2}+b^{y}=c^{z}
Refik Keskin, Zafer Şiar
Let (a,b,c) be a primitive Pythagorean triple, i.e., a^{2}+b^{2}=c^{2} with gcd(a,b,c)=1, a even and b odd. Terai's conjecture says that the Diophantine equation x^{2}+b^{y}=c^{z}…
math.NT2020
Repdigits in k-generalized Pell sequence
Zafer Şiar, Refik Keskin
Let and let be -generalized Pell sequence defined by \begin{equation*}P_{n}^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+...+P_{n-k}^{(k)}\end{equati…
math.NT2020★ 1 cited
An exponential Diophantine equation related to the difference of powers of two Fibonacci numbers
Zafer Şiar
In this paper, we prove that there is no x>=4 such that the difference of x-th powers of two consecutive Fibonacci numbers greater than 0 is a Lucas number.