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arXiv · 1502.04346

Quadratic forms representing the $p$-th Fibonacci number

Pedro Berrizbeitia·Florian Luca·Alberto Mendoza
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Abstract

In this paper, we show that if $p\equiv 1\pmod 4$ is prime, then $4F_p$ admits a representation of the form $u^2-pv^2$ for some integers $u$ and $v$, where $F_n$ is the $n$th Fibonacci number. We prove a similar result when $p\equiv -1\pmod 4$.

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Pedro Berrizbeitia, Florian Luca, Alberto Mendoza. 2015-02-15. Quadratic forms representing the $p$-th Fibonacci number. https://arxiv.org/abs/1502.04346

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