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Probability Level pending

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

n = 1 403 k = 0 4 a 5 n k = 2015 \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 a_k in set a \not= a k a_k in set b when 0<k<2016, or else set a and set b are not distinct. Otherwise, they are.)


The answer is 1323.

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