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2014 preRMO p17, x^2+ax+b = 0 has integer roots , N(b) = 20

Source:

August 9, 2019
algebraIntegerrootsminimum

Problem Statement

For a natural number bb, let N(b)N(b) denote the number of natural numbers aa for which the equation x2+ax+b=0x^2 + ax + b = 0 has integer roots. What is the smallest value of bb for which N(b)=20N(b) = 20?
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