tags : Math

`100mod8 = r`

: 8 is called the modulus,`r`

be +ve no. Sometimes, we are only interested in what the remainder is when we divide A by B. For these cases there is an operator called the modulo operator (abbreviated as mod).

`100mod8`

=`100%8`

=`100/8 ka remainder`

=`100 - (8*12)`

= 4`-100mod8`

=`-100%8`

=`8 - (100/8 ka remainder)`

=`-100 - (8*(-13))`

= 4

## What?

- All integers can be expressed as 0, 1 or 2, or in modulo 3
- Expressing integers in terms of their remainder when divided by 3

- Clock is modulo 12

## Modular exponentiation

- $A_{B}modC=((AmodC)_{B})modC$
- $A_{2}modC=((AmodC)x(AmodC))modC$
- Often we want to calculate A^B mod C for large values of B.
- Unfortunately, A^B becomes very large for even modest sized values for B.