Quadratic forms representing the $p$-th Fibonacci number

Autor:	Berrizbeitia, Pedro, Luca, Florian, Mendoza, Alberto
Rok vydání:	2015
Předmět:	Mathematics - Number Theory 11B39
Druh dokumentu:	Working Paper
Popis:	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 $p\equiv -1\pmod 4$. Comment: 5 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1502.04346 Zobrazit plný text záznamu View this record from Arxiv