This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

# Mod

 Mod[m, n]gives the remainder on division of by . Mod[m, n, d]uses an offset .
• Integer mathematical function, suitable for both symbolic and numerical manipulation.
• 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 , at least so long as and 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 .
• For exact numeric quantities, Mod internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable \$MaxExtraPrecision.
• Mod works with complex numbers, using its definition in terms of Quotient.
• Mod automatically threads over lists.
Remainders mod 3:
 Out[1]=