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