Quadratic residue

Integer that is a perfect square modulo some integer

In number theory, an integer q is a quadratic residue modulo n if it is congruent to a perfect square modulo n; that is, if there exists an integer x such that x 2 ≡ q ( mod n) . {\displaystyle x^{2}\equiv q{\pmod {n}}.} Otherwise, q is a quadratic nonresidue modulo n. Quadratic residues are used in applications ranging from acoustical engineering to cryptography and the factoring of large numbers.

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