Maximum numbers {modulus, arithmetic} can define arithmetics {modular arithmetic} {modulo arithmetic}. If arithmetic-operation result is more than modulus minus one, divide modulus into result until you get remainder less than modulus.
set
In modular arithmetic, modulus is highest number, and zero is lowest number. Modular arithmetic has no negative numbers or fractions. Therefore, many equations have no solutions.
periodicity
Modular arithmetic makes circular set and makes mathematical operations periodic.
congruency
An infinite number of positive integers {congruent integer} have same remainder when divided by modulus. For modulus, all congruent integers form set {residue class, congruency} [x]n or Zn.
Mathematical Sciences>Arithmetic
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Date Modified: 2022.0224