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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