--------- Essay
To explain what is a form, you may think of it as a polynomial.
Revise the material on the lecture notes: you will find 
that the essential results are few, and easily stated. 
Avoid getting into the details of reduction of indefinite 

--------- Problem 1. 
(d) Distinguish between the cases: k=1, k=-1 and |k| >1.

(f) This is much like problem 3 of cwork2.

--------- Problem 3.  
(a) To be equivalent, forms must have the same discriminant.
    Definite forms are equivalent to each other if they are
    equivalent to the unique reduced form in their class.

(b) If Q -> Q' via T and Q' -> Q'' via T', then Q -> Q'' via T T'
    (matrix multiplication).

(c) Compute the matrices that transform b -> a and f -> a. 
    Then invert the latter to get a -> f, and multiply it by 
    the former, to get b -> f.

--------- Problem 5.
(a) Divide into chains by matching the first and last 
    coefficients of the forms. 
(b) The method of part (a) is ambiguous here: 
    divide into chains using continued fractions.

--------- Problem 6.
(b) From the representations of 5 and 13, obtain that of 65.
    From the latter and that of 17, obtain that of 1105, etc.

(c) Formula (1) is a special case of (2) with D=1.

(d) Make sure you represent 4 and 7, not -4 or -7.

--------- Problem 7.
(a) If Q(x,y)=x^2+Dy^2=m, then m is the product of two conjugate 
    quadratic integers.