# 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.)

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