Defining a set of all possible non-congruent integer values

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"Say Peter has discovered that $82$ and $723$ are coprime.

He now believes that the equation below has a solution for all possible integer values of $q$.

$$82p ≡ q\pmod {723},$$

where $p∈$ $\Bbb Z$

Using appropriate and precise mathematical language, define $Q$, the set of all possible non-congruent integer values for $q$.

State, with reason, why Peter is correct regarding the given equation."

With regards to solving this question, I have only found the coefficients of $x$ and $y$ in Bezout's Identity, but am unsure as where to go from there (or if I'm even meant to be there in the first place)