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Find the number of quadratics

Source: Indian RMO 1999 Problem 7

October 26, 2005
quadraticsalgebrapolynomial

Problem Statement

Find the number of quadratic polynomials ax2+bx+cax^2 + bx +c which satisfy the following: (a) a,b,ca,b,c are distinct; (b) a,b,c∈{1,2,3,⋯1999}a,b,c \in \{ 1,2,3,\cdots 1999 \}; (c) x+1x+1 divides ax2+bx+cax^2 + bx+c.
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