text: # Thread: Modulo exercice
  
  1. ## Modulo exercice
  
  Hey again !
  
  I know it is pretty simple but i dont seem to prove it.
  If a=bmodk and c=dmodk then why a-c=(b-d)modk
  
  2. ## Re: Modulo exercice
  
  Originally Posted by grainofsand
  Hey again !
  
  I know it is pretty simple but i dont seem to prove it.
  If a=bmodk and c=dmodk then why a-c=(b-d)modk
  $a=k \cdot n +b \land c = k \cdot m+d \Rightarrow a-c = k \cdot(n-m)+(b-d) \Rightarrow$
  
  $\Rightarrow a-c \equiv b-d \pmod k$
  
  3. ## Re: Modulo exercice
  
  thank you so much !