# Think Simple!

Algebra Level 4

Given $$100$$ reals $$a_{1}, a_{2},\ldots , a_{100}$$ such that $$\displaystyle \sum ^{100}_{i=1}a^{16}_{i} = 2^{32}$$, we have maximum value of $$\displaystyle \sum ^{100}_{i=1}a^{17}_{i}$$ to be of the form $$a^{k}$$, where $$a$$ is a prime and $$k$$ is a positive integer. Find $$(a+k)$$.

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