A binary quadratic form is a quadratic form in two variables having the form Q(x, y) = a x^2 + 2b x y + c y^2, commonly denoted 〈a, b, c〉. Consider a binary quadratic form with real coefficients a, b, and c, determinant D congruent b^2 - a c = 1, and a>0. Then Q(x, y) is positive definite. An important result states that there exist two integers x and y not both 0 such that Q(x, y)<=2/sqrt(3) for all values of a, b, and c satisfying the above constraint.

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