Quadratic residue

A quadratic residue is a concept from number theory, particularly in the study of modular arithmetic.

Quadratic residue codes are a class of error-correcting codes that are derived from the properties of quadratic residues in number theory. These codes are particularly notable in the field of coding theory for their efficiency and ability to detect and correct errors in transmitted data. ### Definition A quadratic residue modulo a prime \( p \) is an integer \( a \) such that there exists some integer \( x \) satisfying the equation \( x^2 \equiv a \mod p \).

Zolotarev's lemma is a result in number theory, particularly in the area of the distribution of prime numbers. It is often used in the context of modular forms and the study of certain types of power sums. The lemma is named after the Russian mathematician V. G. Zolotarev.