Difference between revisions of "2020 USOMO Problems/Problem 3"

(Created page with "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 ≤ a...")
 
 
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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.
 
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.
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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.
 
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.

Latest revision as of 16:57, 28 February 2021

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 ≤ 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.