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: <math> D(f)=b^2-4ac, \quad D(f)\equiv 0,1 \pmod 4. </math>
Gauss proved that for every value ''D'', there are only finitely many classes of binary quadratic forms with discriminant ''D''. Their number is the '''{{vanchor|class number}}''' of discriminant ''D''. He described an algorithm, called '''reduction''', for constructing a canonical representative in each class, the '''reduced form''', whose coefficients are the smallest in a suitable sense. One of the deepest discoveries of Gauss was the existence of a natural '''composition law''' on the set of classes of binary quadratic forms of given discriminant, which makes this set into a finite [[abelian group]] called the '''class group''' of discriminant ''D''. Gauss also considered a coarser notion of equivalence, under which the set of binary quadratic forms of a fixed discriminant splits into several genera of forms and each '''[[Genus of a quadratic form|genus]]''' consists of finitely many classes of forms.
An integral binary quadratic form is called '''primitive''' if ''a'', ''b'', and ''c'' have no common factor. If a form's discriminant is a [[fundamental discriminant]], then the form is primitive.<ref>{{harvnb|Cohen|1993|loc=§5.2}}</ref>
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