GENERALIZED FIBONACCI NUMBERS OF THE FORM 11x(2)

Abstract

Let P >= 3 be an integer and let (U-n) denote generalized Fibonacci sequence defined by U-0 = 0, U-1 = 1 and Un+1 = PUn - Un-1 for n >= 1. In this study, when P is odd, we solve the equation U-n = 11x(2) + 1. We show that only U-1 and U-2 may be of the form 11x(2) + 1.