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- W2016090591 abstract "For a prime $p$, let $Z(p)$ be the smallest positive integer $n$ so that $p$ divides $F_{n}$, the $n$th term in the Fibonacci sequence. Paul Bruckman and Peter Anderson conjectured a formula for $zeta (m)$, the density of primes $p$ for which $m | Z(p)$ on the basis of numerical evidence. We prove Bruckman and Andersonâs conjecture by studying the algebraic group $G : x^{2} - 5y^{2} = 1$ and relating $Z(p)$ to the order of $alpha = (3/2,1/2) in G(mathbb {F}_{p})$. We are then able to use Galois theory and the Chebotarev density theorem to compute $zeta (m)$." @default.
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- W2016090591 date "2014-07-28" @default.
- W2016090591 modified "2023-09-28" @default.
- W2016090591 title "Divisibility properties of the Fibonacci entry point" @default.
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- W2016090591 doi "https://doi.org/10.1090/s0002-9939-2014-12269-6" @default.
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