Modular arithmetic

Description:

• A system of arithmetic for integers, where numbers “wrap around” when reaching a certain value, called the modulus.

Congruent modulo

Corollary:

• Let $m$ be a positive integer and let $a$ and $b$ be integers. Then:
  • $(a+b)\mathrm{mod}m=((a\mathrm{mod}m)+(b\mathrm{mod}m))\mathrm{mod}m$
  • $ab\mathrm{mod}m=((a\mathrm{mod}m)(b\mathrm{mod}m))\mathrm{mod}m$
  • $a^n\mathrm{mod}m=(a\mathrm{mod}m{)}^n\mathrm{mod}m$

Arithmetic modulo