MathDB

Let

k

be a fixed integer greater than 1, and let

{m=4k^2-5}

. Show that there exist positive integers

a

and

b

such that the sequence

(x_n)

defined by x_0=a, x_1=b, x_{n+2}=x_{n+1}+x_n \text{for} n=0,1,2,\dots, has all of its terms relatively prime to

m

.
Proposed by Jaroslaw Wroblewski, Poland

Problem Statement