+41 Let $p(x)$ be the polynomial $(1-x)^a(1-x^2)^b(1-x^3)^c\cdots(1-x^{32})^k$, where $a, b, \cdots, k$ are integers. When expanded in powers of $x$, the coefficient of $x^1$ is $-2$ and the coefficients of $x^2$, $x^3$, ..., $x^{32}$ are all zero. Find $k$.
This is a question from the 1988 USAMO, Problem 5. I didn't understand the solution. Can anyone help?
+118673 I never answer questions when they are presented with unrendered LaTex.
