Mock AIME 4 2006-2007 Problems/Problem 12
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 .
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