Unformatted text preview: its discriminant. (b) Find the source vertex or edge in the topograph of this form. (c) Using the topograph of this form, ±nd all the integer solutions of 92 x 2 − 74 xy + 15 y 2 = 60, and explain why your list of solutions is a complete list. (There are exactly four pairs of solutions ± (x,y) , three of which will be visible in the topograph.) 5. Show that if a quadratic form Q(x,y) = ax 2 + bxy + cy 2 can be factored as a product (Ax + By)(Cx + Dy) with A,B,C,D integers, then Q takes the value 0 at some pair (x,y) n= ( , ) , hence must be either 0hyperbolic or parabolic. Show also, by a direct calculation, that the discriminant of this form is a square. (Do not quote the general fact that a quadratic form is 0hyperbolic or parabolic if and only if it takes the value 0.)...
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 Fall '07
 LOZANOROBLEDO
 Number Theory, Fractions, Conic section, Quadratic form, Continued fraction

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