Mock AIME 4 2006-2007 Problems/Problem 12
Problem
The number of partitions of 2007 that have an even number of even parts can be expressed as , where
and
are positive integers and
is prime. Find the sum of the digits of
.
Solution
Let denote the number of partitions that have an even number of even parts of
. Testing a few small values for
, we see that
.
Based on our observations, we now conjecture* that for every integer
,
So plugging in
, we get
- Insert proof of conjecture here