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1988 USAMO Problem 5

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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?

Jan 20, 2020

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I never answer questions when they are presented with unrendered LaTex.

Jan 20, 2020
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\(p(x)\) be the polynomial

\((1-x)^a*(1-x^2)^b*(1-x^3)^c...(1-x^{32})^k\)

Where a,b,c....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

Jan 20, 2020
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