Math Help - 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 !