MathDB

Define a sequence

F_n

such that

F_1 = 1

F_2 = x

F_{n+1} = xF_n + yF_{n-1}

where and

x

and

y

are positive integers. Suppose

\frac{1}{F_k}= \sum_{n=1}^{\infty}\frac{F_n}{d^n}

has exactly two solutions

(d, k)

with

d > 0

is a positive integer. Find the least possible positive value of

d

Problem Statement