Binary quadratic form: Difference between revisions

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is an automorphism of the form <math>f = x^2 - 2y^2</math>. The automorphisms of a form form a [[subgroup]] of <math>\mathrm{SL}_2(\mathbb{Z})</math>. When ''f'' is definite, the group is finite, and when ''f'' is indefinite, it is infinite and [[cyclic group|cyclic]].

==RepresentationsRepresentation==

We say that aA binary quadratic form <math>q(x,y)</math> '''represents''' an integer <math>n</math> if it is possible to find integers <math>x</math> and <math>y</math> satisfying the equation <math>n = q(x,y).</math> Such an equation is a '''representation''' of {{math|''n''}} by {{math|''q''}}.

=== Examples ===