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integer roots of P(P(x)) when P(x) has n roots included 0

Source: Czech and Slovak Match 1998 P2

October 1, 2017
integer rootInteger Polynomialalgebra

Problem Statement

A polynomial P(x)P(x) of degree n≥5n \ge 5 with integer coefficients has nn distinct integer roots, one of which is 00. Find all integer roots of the polynomial P(P(x))P(P(x)).
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