hi Harold,
In effect, that was my point in post 7.
The following are all equivalent mod 5
-12, -7, -2, 3, 8, 13, 18 ......
Basically just add 5.
If you follow my link to Wiki you will see that two definitions are possible and there are even more variations amongst computer languages.
Your brother is right using the 'Euclidean division' definition ... under this no negatives are allowed.
Which is why I think you need to check with your teacher / tutor and see what definition is required.
Bob