IMO 2005 Q4 #
Problem: Determine all positive integers relatively prime to all the terms of the infinite sequence
a n = 2 ^ n + 3 ^ n + 6 ^ n - 1
, for n ≥ 1
.
This is quite an easy problem, in which the key point is a modular arithmetic calculation with
the sequence a n
relative to an arbitrary prime.
Key lemma (a modular arithmetic calculation): Given a prime p
other than 2
or 3
, the
p - 2
th term of the sequence has p
as a factor.