# A Question on Polynomials, part 2

Algebra Level 5

Given that $$f$$ is a polynomial of degree 100 and that $$f(k)=2^k$$ for $$k=1, 2, \ldots , 101$$. Find the last five digits of $$f(102)$$.

You may use the fact that the llast five digits of $$2^{101}$$ is 10752.

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