1988 USAMO Problems/Problem 5

Problem

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 $k$ .

Solution

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1988 USAMO (Problems • Resources)
Preceded by Problem 4	Followed by Last Question
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1988 USAMO Problems/Problem 5

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