Work out quadratic residue instantly with clear inputs, formula shown and shareable results.
A quadratic residue modulo m is a value congruent to some perfect square. Unlike ordinary square roots, a modular square root may have zero, one, two or more solutions depending on the factorisation of m.
Quadratic residue
a is a residue mod m if x² ≡ a (mod m) has a solution
Yes, with roots 3 and 20, since 20 ≡ −3 and (−3)² = 9.
For composite moduli the Chinese remainder theorem multiplies the root counts of each prime power factor.