Modulo of a negative number

Question

Why is

$347 \bmod 6 = 5$

but

$-347 \bmod 6 = 1$

What is the difference?

$347\equiv 5 \pmod 6\implies -347\equiv -5 \pmod 6$ But we also have $-5\equiv 1 \pmod 6$. — lulu, May 14 '16 at 01:31

score 1 · Answer 1 · answered May 14 '16 at 01:31

1

If $a\equiv b\pmod n$, then $(-a)\equiv (-b)\pmod n$. Thus $-347 \equiv -5 \equiv 1\pmod 6$.

answered May 14 '16 at 01:31

choco_addicted

score 1 · Answer 2 · answered May 14 '16 at 05:32

1

Hint:-

The basic difference lies here-

$(a-b)\neq(-a-b)\text{ or}-(a+b)$

$(347-5)=342$ but $(-347-1)=-348$ both of which are divisible by $6$.

answered May 14 '16 at 05:32

Soham

So why is the answer + 1 and not - 5? – the_prole May 14 '16 at 06:03
@the_prole Which $-5$...please add a detailed question.... – Soham May 14 '16 at 06:28
Here http://math.stackexchange.com/questions/1784660/modulo-with-negative-numbers – the_prole May 14 '16 at 06:35
@the_prole Check my answer...Hope it solves your problem!! – Soham May 14 '16 at 06:43

2 Answers2