MathDB

M 25

Source:

May 25, 2007

Recursive Sequences

Problem Statement

Let

\{a_{n}\}_{n \ge 1}

be a sequence of positive integers such that

0 < a_{n+1}-a_{n}\le 2001 \;\; \text{for all}\;\; n \in \mathbb{N}.

Show that there are infinitely many pairs

(p, q)

of positive integers such that

p>q

and

a_{q}\; \vert \; a_{p}

.

Back to Problems View on AoPS