A binary quadratic form is a quadratic form in two variables having the form
 |
(1)
|
commonly denoted 
.
Consider a binary quadratic form with real coefficients 
, 
, and 
, determinant
 |
(2)
|
and 
.
Then 
is positive definite. An important
result states that there exist two integers 
and 
not both 0 such that
 |
(3)
|
for all values of 
,
,
and 
satisfying the above constraint (Hilbert and Cohn-Vossen 1999, p. 39).
