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If the sum of the coefficients of all even powers of $x$ in the product $(1 + x + x^2 + \ldots + x^{2n})(1 - x + x^2 - x^3 + \ldots + x^{2n})$ is 61, then $n$ is equal to ____.
Put $x = 1$ and $x = -1$: $2n + 1 = 61$, $n = 30$.
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