Congruence of Sum with Constant

Theorem
Let $$a, b \in \Z$$ and $$n \in \N$$.

Let $$a$$ be congruent to $b$ modulo $n$, i.e. $$a \equiv b \pmod n$$.

Then $$\forall c \in \Z: a + c \equiv b + c \pmod n$$.

Proof
Follows directly from the definition of Modulo Addition:

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