DIVISIBILITY PROPERTIES OF THE FIBONACCI ENTRY POINT

作者：Cubre Paul^*; Rouse Jeremy

来源：Proceedings of the American Mathematical Society, 2014, 142(11): 3771-3785.

DOI：10.1090/S0002-9939-2014-12269-6

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 zeta(m), the density of primes p for which m vertical bar Z(p) on the basis of numerical evidence. We prove Bruckman and Anderson%26apos;s 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) is an element of G(F-p). We are then able to use Galois theory and the Chebotarev density theorem to compute zeta(m).

• 出版日期2014-11