2003 OIM Problems/Problem 6

Problem

Sequences $(a_n)_{n \ge 0}$ , and $(b_n)_{n \ge 0}$ are defined by:

$a_0=1 \text{, }b_0=4\text{, and}$

$a_{n+1}=a_n^{2001}+b_n\text{, for }n \ge 0\text{.}$

$b_{n+1}=b_n^{2001}+a_n\text{, for }n \ge 0\text{.}$

Show that 2003 does not divide any of the terms of these sequences.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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