Information provided by the grader:

HW1:

One mistake happened a lot: on question #16, section 1.4,
only 3 students actually showed that the remainder is
bs+r (by showing that 0 =< bs+r < bc). Everyone else
just showed that a=bct+(bs+r), and assumed it was enough.

Comment: On question 28 (section 7.1) a lot of students
did the following:  m | n, so there is k such that n=km.
Then, since Phi is multiplicative, Phi(n)=Phi(k)Phi(m),
so Phi(m) | Phi(n). This would be true only if (k,m)=1
(f multiplicative means f(ab)=f(a)f(b) whenever (a,b)=1),
what we can not assume in general.