--------- Problem 3.  
    Change sign.

--------- Problem 4. 
(a) You must perform long division of two polynomials 
    (in the indeterminate n).

(b) Numerator and denominator are non-monic polynomials
    (the leading coeff is not 1). So Euclid's algorithm
    does not apply, and the remainder has the same degree
    as the divisor.

(c) Factor the polynomial n^k-1.

--------- Problem 5.
(a) To carry out the inductive step, you must compute p_{n+1}/p_n.
    Use theorem 1.2 for the numerator, leaving the denominator unchanged.

--------- Problem 6. 
(a) Use problem 5

(c) Show that q_n=p_{n-1}, where p_n=p and q_n=q.
    Then use problem 5.