PreprintCC BY 4.0arXiv
On the nonnegative integer solutions to the equation Fn2+Fm=2a
Abstract
The Diophantine equation Fnx+Fmy=2a, where Fk denotes the k-th Fibonacci number and n,m,a∈ ℤ≥0, has attracted attention in recent years. The cases (x,y)=(1,1) and (x,y)=(2,2) were completely resolved by Bravo and Luca, and by Jeong and Park, respectively. In this note, we investigate the mixed exponent case (x,y)=(2,1) and we completely determine all nonnegative integer solutions.
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BibTeX
@misc{mandal2026nonnegative,
title = {{On the nonnegative integer solutions to the equation $F_n^2+F_m=2^a$}},
author = {Sagar Mandal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18894},
eprint = {2610.18894},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18894},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the nonnegative integer solutions to the equation F_n^2+F_m=2^a
AU - Sagar Mandal
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.18894
UR - https://arxiv.org/abs/2610.18894
AB - The Diophantine equation F_n^x+F_m^y=2^a, where F_k denotes the k-th Fibonacci number and n,m,a∈ ℤ_≥0, has attracted attention in recent years. The cases (x,y)=(1,1) and (x,y)=(2,2) were completely resolved by Bravo and Luca, and by Jeong and Park, respectively. In this note, we investigate the mixed exponent case (x,y)=(2,1) and we completely determine all nonnegative integer solutions.
ER -