R. Keskin

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20172022

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math.NT2018

On the Exponential Diophantine Equation $(a^{2} - 2) (b^{2} - 2) = x^{2}$

Zafer Şiar, Refik Keskin

In this paper, we consider the equation $(a^{n} - 2^{m}) (b^{n} - 2^{m}) = x^{2}$ . By assuming the abc conjecture is true, in [8], Luca and Walsh gave a theorem, which implies that the above eq…

math.NT2018

A Note On the Exponential Diophantine Equation (a^n-1)(b^n-1)=x^2

Refik Keskin

In 2002, F. Luca and G. Walsh solved the Diophantine equation in the title for all pairs (a,b) such that 1<a<b<101 with some exceptions. There are sixty nine exceptions. In this pa…

On the Exponential Diophantine Equation (a2−2)(b2−2)=x2

A Note On the Exponential Diophantine Equation (a^n-1)(b^n-1)=x^2

On the Exponential Diophantine Equation $(a^{2} - 2) (b^{2} - 2) = x^{2}$