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Omni-MATH / Let p be an odd prime. An integer x is called a quadratic non-residue if p does not divide x−t² for any integer t . Denote by A the set of all integers a such that 1≤a<p , and both…

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problem

Let pp be an odd prime. An integer xx is called a quadratic non-residue if pp does not divide x−t2x - t^2 for any integer tt . Denote by AA the set of all integers aa such that 1≤a<p1 \le a < p , and both aa and 4−a4 - a are quadratic non-residues. Calculate the remainder when the product of the elements of AA is divided by pp .
Plain-text mathematical notation (without MathML)
Let p be an odd prime. An integer x is called a quadratic non-residue if p does not divide x−t² for any integer t .
Denote by A the set of all integers a such that 1≤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 .
Original LaTeX notation
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 $p$ .

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Source and history

task_id
bd2d56b1-2357-5336-8604-2b57fa0129dd
task_key
test--bd2d56b1-2357-5336-8604-2b57fa0129dd
task_revision_id
1
config / split
/ test

Official source

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