2020 USAMO Problems/Problem 3

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)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5
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2020 USAMO Problems/Problem 3

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