2-ADIC VALUATIONS OF GENERALIZED FIBONACCI NUMBERS OF ODD ORDER

摘要

Let Tn denote the generalized Fibonacci number of order k defined by the recurrence Tn = Tn1 + Tn2 + · · · + Tnk for n k, with initial conditions T0 = 0 and Ti = 1 for 1 ? i < k. In this paper we establish the 2-adic valuation of Tn in almost all cases when k is odd. Our results settle some conjectures of Lengyel and Marques.