# RMO Practice Problems - Algebra 1

Algebra Level 5

Let $$P(x)$$ be a polynomial of degree 2015 which satisfies $$P(k) = 2^{k}$$ for all $$k=0,1,2,3, \ldots, 2015$$. If the value of $$P(2016)$$ can be expressed as

$a^{b} - c,$

where $$a$$ and $$c$$ are coprime integers and $$a$$ is a prime, find the value of $$a+b+c$$.

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