Mod
Mod[m, n] gives the remainder on division of m by n.
Mod[m, n, d] uses an offset d.
For integers 
and 
Mod[m, n] lies between 0 and 
.
Mod[m, n, 1] gives a result in the range 
to 
, suitable for use in functions such as Part.
Mod[m, n, d] gives a result 
such that 
and 
.
The sign of Mod[m, n] is always the same as the sign of n, at least so long as m and n are both real.
Mod[m, n] is equivalent to m - n Quotient[m, n].
Mod[m, n, d] is equivalent to m - n Quotient[m, n, d].
The arguments of Mod can be any numeric quantities, not necessarily integers.
Mod[x, 1] gives the fractional part of x.
For exact numeric quantities, Mod internally uses numerical approximations to establish its result.
See The Mathematica Book on the web: Section 1.1.3 and Section 3.2.4.
See also: PowerMod, Quotient, FractionalPart, PolynomialMod, PolynomialRemainder, Xor.
Further Examples
