For discussing Olympiad Level Number Theory problems
swapnil saha
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Unread post by swapnil saha » Sat Aug 10, 2013 5:49 pm

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

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Re: modulo

Unread post by harrypham » Sun Aug 11, 2013 9:06 pm

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 $a+c \equiv b+c \pmod{m}$.

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