Modulo

Abstract

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• Returns the remainder or signed remainder of a division

Congruence Modulo

• Congruence means “the same”

• Congruence Modulo basically means two numbers have the same remainder when divided by the same Factor

  
  

• Represented with $\equiv$

• $a\equiv b$ (mod $m$) is read as ”$a$ is congruent to $b$ modulo $m$

• $a\equiv b$ (mod $m$) means that $a$ and $b$ have the same remainder when divided by $m$

  
  

• $a\equiv b$ (mod $m$) is true if and only if $m|(a-b)$

• $a$ and $b$ are in the same Equivalence Relation modulo $m$, $[a{]}_m=[b{]}_m$