D ec 1 99 9 PRIME DIVISORS OF THE LAGARIAS SEQUENCE

نویسنده

  • Peter Stevenhagen
چکیده

We solve a 1985 challenge problem posed by Lagarias [5] by determining, under GRH, the density of the set of prime numbers that occur as divisor of some term of the sequence {xn}∞ n=1 defined by the linear recurrence xn+1 = xn + xn−1 and the initial values x0 = 3 and x1 = 1. This is the first example of a ‘non-torsion’ second order recurrent sequence with irreducible recurrence relation for which we can determine the associated density of prime divisors.

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تاریخ انتشار 2008