2011 PuMAC Problems/Algebra Problem A1

Note that in a polynomial $\displaystyle\sum^{n}_{i=0} a_ix^i$, $x=1$ gives $\displaystyle\sum^{n}_{i=0} a_i$, which is the sum of the coefficients.

Therefore, the sum of the coefficients of $(63x-61)^4$ is $(63-61)^4 = 2^4 = \boxed{16}$

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