2005 Canadian MO Problems/Problem 5
Problem
Let's say that an ordered triple of positive integers is
-powerful if
,
, and
is divisible by
. For example,
is 5-powerful.
- Determine all ordered triples (if any) which are
-powerful for all
.
- Determine all ordered triples (if any) which are 2004-powerful and 2005-powerful, but not 2007-powerful.