$6 \equiv 6 \pmod{7}$ or $6 \equiv -1 \pmod{7}$?

Question

Just a quick question: Is $6 \equiv 6 \pmod{7}$ or $6 \equiv -1 \pmod{7}$?

I'm just trying to figure out whether there was an error in the answer by Jazzachi in this question.

Thanks.

Answer 1

$$6 \equiv 6 \pmod{7}$$ and $$6 \equiv -1 \pmod{7}$$ are both true.

As you know the definition is $$a\equiv b\pmod {n} \iff n|(b-a)$$

For example $$35 \equiv 30 \pmod{5}$$ because $$5| 30-35$$