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3x^2 - px + q = 0 , where p.q are primes and has two rational solutions

Source: 1993 ITAMO p2

January 31, 2020
quadratic trinomialtrinomialQuadraticnumber theoryRational rootsrationalprimes

Problem Statement

Find all pairs (p,q)(p,q) of positive primes such that the equation 3x2āˆ’px+q=03x^2 - px + q = 0 has two distinct rational roots.