Problem

Source: 2023 China South East Mathematical Olympiad Grade 10 P8 CSMO

Tags: algebra, polynomial, geometry, geometric transformation



Let $p(x)$ be an $n$-degree $(n \ge 2)$ polynomial with integer coefficients. If there are infinitely many positive integers $m$, such that $p(m)$ at most $n -1$ different prime factors $f$, prove that $p(x)$ has at most $n-1$ different rational roots . a help in translation is welcome


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