Is it true that if $ -p \equiv -1 \pmod q $, then $p \equiv 1 \pmod q $?

Question

Is it true that if $ -p \equiv -1 \pmod q $, then $p \equiv 1 \pmod q $? p and q are prime numbers.

Answer 1

Yes. $-p = -1 + nq$, so $p = 1-nq = 1 + (-n) \times q$.