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Given 100 100100 reals a1,a2,…,a100 a_{1}, a_{2},\ldots , a_{100} a1,a2,…,a100 such that ∑i=1100ai16=232\displaystyle \sum ^{100}_{i=1}a^{16}_{i} = 2^{32}i=1∑100ai16=232, we have maximum value of ∑i=1100ai17\displaystyle \sum ^{100}_{i=1}a^{17}_{i}i=1∑100ai17 to be of the form ak a^{k} ak, where a a a is a prime and k k k is a positive integer. Find (a+k) (a+k) (a+k).
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