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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