What does $\text{mod}\ m$ in $a \equiv b (\text{mod}\ m)$ means

Question

I am trying to do example 3.6 from this http://www.cs.fsu.edu/~lacher/courses/MAD3105/lectures/s1_3equivrel.pdf script, but I am not sure what does $(\text{mod}\ m)$ means.

Can somebody explain it to me. Thanks.

$a\equiv b\pmod m$ means that $a-b$ is an integer multiple of $m$. — MJD, Feb 12 '14 at 14:04

score 2 · Accepted Answer · answered Feb 12 '14 at 13:58

2

$m\mid a-b$ as a whole meaning of $a\equiv b$ mod (m)

answered Feb 12 '14 at 13:58

Myshkin

score 1 · Answer 2 · answered Feb 12 '14 at 14:02

1

a= k*m + b ; b is the rest of the euclidian division of a by m

answered Feb 12 '14 at 14:02

mounaim

Not true. If it were $\ b = (a\ {\rm mod}\ m)\ $ then you could say that $,b,$ is the remainder of $,a,$ modulo $,m.,$ But the notation $,a\equiv b\pmod{m},$ means precisely that $,m\mid a-b,,$ which does not imply anything about the size of $,a,b.\ \ $ – Bill Dubuque Feb 12 '14 at 15:35

2 Answers2