2020 USOMO Problems/Problem 3: Difference between revisions
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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. | ||
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 15:57, 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.
