Definition of q congruent to 1 (mod p)

Question

What is the meaning of q $\equiv 1\pmod p$?

If I were to write this as a definition, how would I explain with this means?

$a\equiv b\pmod c$ means that $c$ is a divisor of $a-b$. – Angina Seng May 25 '18 at 19:16 — Angina Seng, May 25 '18 at 19:16

score 1 · Answer 1 · answered May 25 '18 at 19:16

1

The meaning is that $p$ divides $q$ with remainder $1$.

answered May 25 '18 at 19:16

D.B.

Thanks. I forgot to clarify in the original question, but I was supposed to write the meaning of it in terms of divisibility. But, it seems like you did just that. – Ryan May 25 '18 at 19:24

score 1 · Answer 2 · answered May 25 '18 at 19:18

1

Maybe the simplest way to phrase it would be:

If you subtract 1 from q, you get a multiple of p.

answered May 25 '18 at 19:18

user1390

score 0 · Answer 3 · answered May 25 '18 at 19:21

0

It means $p$ divides $q-1$.

$$q \equiv 1 \mod p$$

$$\implies q-1 \equiv 0 \mod p$$

$$\implies p | (q-1) $$

answered May 25 '18 at 19:21

Hindu

3 Answers3