Mod

Mod[ m, n ] returns the remainder when dividing two integers.

Usages

`Mod[ m, n ]`

Mod[ m, n ] returns the remainder when m is divided by n. The remainder is always between 0 and |n|-1, also for negative numbers. The result is 0 when n divides m, so Mod is often used to test divisibility.

Example	in	out
`17 = 3 · 5 + 2`.	`Mod[ 17, 5 ]`	`2`
`5` divides `15`.	`Mod[ 15, 5 ]`	`0`
A negative number: `-8 = -3 · 3 + 1`.	`Mod[ -8, 3 ]`	`1`
A negative divisor gives the same result as a positive one.	`Mod[ 8, -3 ]`	`2`
Test if a script variable is even.	`n := 12 r := Mod[n, 2] == 0`	`r = True`

`Mod[ list, n ]`

If an argument is a list, the remainder is calculated for each element.

Example	in	out
The remainders when dividing by `3`.	`Mod[ {10, 11, 12}, 3 ]`	`{1, 2, 0}`

Details

Invalid input	Result
`Mod[ 17, 0 ]`	Error: the second argument should be a non-zero natural number
`Mod[ 17 ]`	Error: the number of arguments should be 2
`Mod[ 17.5, 5 ]`, `Mod[ x, 5 ]`	Left unevaluated: the arguments must be integers.