USAMO 1977 Problem 1

Day 1
Answer

For which positive integers $\mathrm{a}, \mathrm{b}$ does $\left(\mathrm{x}^{\mathrm{a}}+\ldots+\mathrm{x}+1\right)$ divide $\left(\mathrm{x}^{\mathrm{ab}}+\mathrm{x}^{\mathrm{ab}-\mathrm{b}}+\ldots+\mathrm{x}^{2 b}+\mathrm{x}^{\mathrm{b}}+1\right)$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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a+1 \text{ and } b \text{ relatively prime}

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