Izvorni znanstveni članak

https://doi.org/10.64785/mc.30.2.2

On the Diophantine equation \(F_{n}^{2}+F_{m}^{2}=2^{\alpha}\)

Ga-Hyun Jeong ; Department of Mathematics Education, Kyungnam University, Republic of Korea
Poo-Sung Park ; Department of Mathematics Education, Kyungnam University, Republic of Korea

Sažetak

Let \(F_{n}\) be the 𝑛-th Fibonacci number. In this paper, we show that the only nonnegative solutions (𝑛, 𝑚, 𝑎)
of the Diophantine equation \(F_{n}^{2}+F_{m}^{2}=2^{\alpha}\) with 𝑛 ≥ 𝑚 ≥ 0 are (1, 0, 0), (2, 0, 0), (3, 0, 2), (6, 0, 6), (1, 1, 1), (2, 1, 1), (2, 2, 1), (3, 3, 3), (6, 6, 7).

Ključne riječi

Fibonacci numbers; Diophantine equation; linear forms in logarithms; reduction method

Hrčak ID:

335660

URI

https://hrcak.srce.hr/335660

Datum izdavanja:

22.9.2025.

Posjeta: 557 *