Y by Com10atorics, Adventure10, Mango247, and 1 other user
Let
be a fixed integer greater than 1, and let
. Show that there exist positive integers
and
such that the sequence
defined by
has all of its terms relatively prime to
.
Proposed by Jaroslaw Wroblewski, Poland





![\[x_0=a,\quad x_1=b,\quad x_{n+2}=x_{n+1}+x_n\quad\text{for}\quad n=0,1,2,\dots,\]](http://latex.artofproblemsolving.com/b/2/6/b26931e97d94c1b445358b3338b9b3918f3f270c.png)

Proposed by Jaroslaw Wroblewski, Poland
This post has been edited 1 time. Last edited by djmathman, Aug 1, 2015, 2:54 AM
Reason: formatting
Reason: formatting