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Latest revision as of 10:15, 31 July 2023

Problem

Let $p$ be an odd prime. An integer $x$ is called a quadratic non-residue if $p$ does not divide $x - t^2$ for any integer $t$.

Denote by $A$ the set of all integers $a$ such that $1 \le a < p$, and both $a$ and $4 - a$ are quadratic non-residues. Calculate the remainder when the product of the elements of $A$ is divided by $p$.

Solution

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2020 USAMO (Problems • Resources)
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Problem 2 		Followed by
Problem 4
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All USAMO Problems and Solutions

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