On the Diophantine equation \(F_{n}^{2}+F_{m}^{2}=2^{\alpha}\)
Let ???????? be the ????-th Fibonacci number. In this paper, we show that the only nonnegative solutions (????, ????, ????) of the Diophantine equation ???? 2 ???? + ???? 2 ???? = 2 ???? with ???? ≥ ???? ≥ 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)
Authors
- Poo-Sung Park (ORCID: https://orcid.org/0009-0008-2963-0408)
- Ga-Hyun Jeong (ORCID: https://orcid.org/0009-0004-5063-2900)
Institutions
- Kyungnam University (KR)
Publication Details
- Journal
- Mathematical communications
- Published
- 2025-09-22
- DOI
- https://doi.org/10.64785/mc.30.2.2
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Research Foundation
- National Research Foundation of Korea
- Ministry of Science and ICT, South Korea