Abstract. For a prime p, let Z(p) be the smallest positive integer n so that p divides F n , the nth term in the Fibonacci sequence. Paul Bruckman and Peter Anderson conjectured a formula for ζ(m), the density of primes p for which m|Z(p) on the basis of numerical evidence. We prove Bruckman and Anderson's conjecture by studying the algebraic group G : x 2 − 5y 2 = 1 and relating Z(p) to the order of α = (3/2, 1/2) ∈ G(F p ). We are then able to use Galois theory and the Chebotarev density theorem to compute ζ(m).

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