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.

score 5 · Accepted Answer · answered Jun 03 '16 at 10:42

5

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

answered Jun 03 '16 at 10:42

Patrick Stevens

2

Note also that as Patrick Stevens' answer makes clear, this is true even if we do not require that $p$ and $q$ be prime. – Ceph Jun 03 '16 at 10:47

1 Answers1