# 3. Looks hard? Try expanding it...

**Discrete Mathematics**Level pending

Given that \(a_m\) (m<2016) are nonegative integers, how many distinct sets of \(a_m\) are there such that:

\(\prod_{n=1}^{403}\sum_{k=0}^4 a_{5n-k}=2015\)

Add the digits of the big number up.

Details: In this case, 'distinct' means that all elements in two sets cannot be equal to each other in a fixed order. (i.e. \(a_k\) in set a \(\not=\) \(a_k\) in set b when 0<k<2016, or else set a and set b are not distinct. Otherwise, they are.)