> ((D%C)+(B%C)) = (D+B) % C
This is wrong. You need an extra %C on the left hand side for that identity to work:
((D%C)+(B%C))%C = (D+B) % C
This is wrong. You need an extra %C on the left hand side for that identity to work:
((D%C)+(B%C))%C = (D+B) % C