# Seeking proper terminology

Consider

$\qquad a = b^2 \pmod c$.

Are there special "names" for $a$ and/or $b$? I mean something like '$b$ is a modular root of $a$' or similar.

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$a$ is called a quadratic residue modulo $c$ in this case. I doubt there is a name for $b$ besides "a solution to the congruence $x^2\equiv a\pmod c$".