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

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also