Mod[m, n]
gives the remainder on division of m by n.

Mod[m, n, d]
uses an offset d.


  • Integer mathematical function, suitable for both symbolic and numerical manipulation.
  • For integers m and n, Mod[m, n] lies between and n-1.
  • Mod[m, n, 1] gives a result in the range to n, 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. »
  • For positive x, Mod[x, 1] gives the fractional part of x.
  • 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.
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