# A Question on Polynomials, part 3

Algebra Level 5

Given that $$f$$ is a polynomial of degree 100 and that $$f(k)=k\times 2^k$$ for $$k=1, 2, \ldots , 101$$.

Given that $$f(102)=102\times 2^{102} - A$$, where $$A$$ is a positive integer. Find the value of $$A$$.

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