I have a problem with an exercise. I have the two following sentences I have to determine if they are true or false.
If $a<b$ and the remainder of $b$ and $a$ divided by $c$ are equal then $c\mid(b-a)$
If $a<b$ and the remainder of $b$ and $a$ divided by $c$ are equal then $c\mid b-a$
I think the first is true. But I can't understand what's the different when removing the brackets?
Thanks.
EDITED! I was mistaken copying the questing. Sorry! Now its correct
The first one is true even if you remove the hypothesis that $a<b$.
I also see no difference between the assertions.