On solutions of some Diophantine equations

Year 2025, Early View, 1 - 1

Refik Keskin , Kübra Ged , Fatih Erduvan

https://doi.org/10.35378/gujs.1378010

Abstract

Let k and p be prime numbers with p>2. In this note, we find all positive integer solutions to the Diophantine equations

x^2-kxy-y^2=±k,
x^2-(k^2+4) y^2=±4k,
x^2-2pxy-y^2=±2p,
x^2-kxy-y^2=±k(k^2+4)

in terms of generalized Fibonacci and Lucas numbers.

Keywords

Diophantine equations, Generalized Fibonacci numbers, Generalized Lucas numbers

References

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