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2024 Alg/NT Problem 6

Source:

April 14, 2024
algebra

Problem Statement

Integers a,ba, b satisfy the following property: the line y=2x+aby = 2x + ab passes through all intersection points of the two parabolas given by y = x^2 + 2x + a,   y = 2x^2 +bx, which intersect at least once. How many such (a,b)(a, b) satisfy ∣ab∣≤100|ab| \leq 100?
Proposed by Justin Hsieh
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