quadratic residue

Noun

quadratic residue (plural quadratic residues)

1. (modular arithmetic) For a given positive integer n, any integer that is congruent to some square m² modulo n.
   • There are many small tables of quadratic residues giving for the first few primes p the positive quadratic residues of p arranged in order of their size.1941, Derrick Henry Lehmer, Guide to Tables in the Theory of Numbers, National Research Council, page 52
   • If we now make the assumption that q is a quadratic residue of all odd primes z not greater than 2m + 1, then it follows from earlier theorems (§37) that the prime q, since it is ≡ 1 (mod 8) and hence a quadratic residue of each power of 2, is also a quadratic residue of each number which has no...1991, John Stillwell (translator), Peter Gustav Lejeune Dirichlet, Lectures on Number Theory, [1863, Vorlesungen über Zahlentheorie], American Mathematical Society, London Mathematical Society, page...