Information provided by the grader:

HW #8
There's a common mistake a lot of students are making:
whenever they need to show that the order of an element "a" 
(mod m) is k, they just show that a^k = 1 (mod m), but
don't check that a^j != 1 (mod m) for j less than k. This caused 
mistakes on questions with primitive roots also.