Modulus
The word modulus has several different meanings in mathematics with respect to complex numbers, congruences, elliptic integrals, quadratic invariants, sets, etc.
The modulus of a congruence a=b (mod m) is the number m. It is the "base" with respect to which a congruence is computed (i.e., m gives the number of multiples of a that are "thrown out"). For example, when computing the time of day using a 12-hour clock obtained by adding four hours to 9:00, the answer, 1:00, is obtained by taking 9+4=1 (mod 12) (i.e., adding the hours with modulus 12).
In many computer languages (such as FORTRAN or the Wolfram Language), the common residue of b (mod m) is written mod(b,m) (FORTRAN) or Mod[b,m] (Wolfram Language).
See also
Complex Modulus, Congruence, Elliptic Modulus, Quadratic Invariant Modulus, Set ModulusRelated Wolfram sites
http://functions.wolfram.com/IntegerFunctions/Mod/Explore with Wolfram|Alpha
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Cite this as:
Weisstein, Eric W. "Modulus." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Modulus.html