# Modulo exercice

• Jan 14th 2012, 11:43 PM
grainofsand
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
• Jan 15th 2012, 12:35 AM
princeps
Re: Modulo exercice
Quote:

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

$a=k \cdot n +b \land c = k \cdot m+d \Rightarrow a-c = k \cdot(n-m)+(b-d) \Rightarrow$

$\Rightarrow a-c \equiv b-d \pmod k$
• Jan 15th 2012, 12:43 AM
grainofsand
Re: Modulo exercice
thank you so much !