wording of modular arithmetic

Question

Should we say find the inverse of a residue modulo n or find the inverse of an integer modulo n? I am trying to get the precise wording for an elementary number theory course.

Answer 1

$ab \equiv 1 \pmod n$ is read $ab$ is congruent to $1 \pmod n$

and $b$ is the modular multiplicative inverse of $a \pmod{n}$ such that:

$a^{-1} \equiv b \pmod{n}$