Is the following valid?

Proove that all integers prior to N that are co-primes to N (including 1) their sum is divisible by N

Example

Let

$\displaystyle

N=8

$

Then

$\displaystyle

1+3+5+7=16

$

and

$\displaystyle

16 \quad mod \quad 8=0

$

Thank you all for your time and response