modulo

For discussing Olympiad Level Number Theory problems
swapnil saha
Posts: 2
Joined: Wed Sep 19, 2012 6:02 pm

modulo

what is modulo(mod) and how it is used?

harrypham
Posts: 12
Joined: Wed Aug 31, 2011 12:31 pm
Location: Vietnam
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Re: modulo

We have $m|a-b$ with $m,a,b \in \mathbb{Z}, \; m \ne 0$ then we write $a \equiv b \pmod{m}$.
Some property:
$a \equiv b \pmod{m}, \; b \equiv c \pmod{m}$ then $a \equiv c \pmod{m}$.
$a \equiv c \pmod{m}, \; b \equiv d \pmod{m}$ then $ab \equiv cd \pmod{m}$.
$a \equiv b \pmod{m}$ then $a+c \equiv b+c \pmod{m}$.