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IMO Shortlist 2012, Algebra 4

Source: IMO Shortlist 2012, Algebra 4

July 29, 2013
algebrapolynomialnumber theoryRational rootsIMO Shortlistreal analysis

Problem Statement

Let ff and gg be two nonzero polynomials with integer coefficients and deg⁡f>deg⁡g\deg f>\deg g. Suppose that for infinitely many primes pp the polynomial pf+gpf+g has a rational root. Prove that ff has a rational root.
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