Compute the number of positive integers a for which there exists an integer b, 0 ≤ b ≤ 2002, such that both of the quadratics x^2 + ax + b and x^2 + ax + b + 1 have integer roots.
#Number of positive integers
cursive pier
quick bluffBOT
Compute the number of positive integers a for which there exists an integer b, 0...
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turbid tundra
Have you done anything so far? I would consider discriminants.
cunning path
if they have integar roots , think about the sum and the product of those roots of a quardratic function in terms of its coefficient. x^2 + px + q, the sum of the roots is -p and the product of the roots is q, then compare the roots of the two quadratics and notice how they are related