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This is from a math contest. I have solved it, but I'm posting it on here because I think that it would be a good challange problem for precalculus courses. Also, it's kind of fun.

Write the polynomial $ \prod_{n=1}^{1996}(1+nx^{3^n})$=$\sum_{n=0}^m a_nx^{k_n}$, where the $k_n$ are in increasing order, and the $a_n$ are nonzero. Find the coefficent $a_{1996}$.

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    Hint: If you write $k_n$ in base $3$, then it has the same digits as if you wrote $n$ is base $2$.2012-07-06

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