Modular arithmetic

• Given an integer $n>1$, called a modulus, two integers $a$ and $b$ are said to be congruent modulo $n$, if $n$ is a divisor of their difference; that is, if there is an integer $k$ such that $a-b=kn$
  • Congruence modulo $n$ is denoted $a\equiv b(\mathrm{mod}n)$
  • Congruence modulo $n$ is a congruence relation, meaning that it is an Equivalence relation that is compatible with the operations of addition, subtraction, multiplication, translation, scaling and exponentiation