RMO Practice Problems - Algebra 1

Algebra Level 5

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

abc,a^{b} - c,

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

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