Here is a hint. If is a primitive root, then all primitive roots of mod are where and .
This one should be approached like the one above. But this one is tricker. Let us focus on an easier case first, say . Now is a primitive then is a primitive root too (prove this). And so the entire sum can be paired to cancel out mod . And so we are left with zero. Notice that if then divides and so . Now you need to consider other cases.Show that the sum of all primitive roots modulo is congruent to modulo .