Integer Polynomial with P(a)=b, P(b)=c, and P(c)=a
Source: 1974 USAMO Problem 1
March 13, 2010
algebrapolynomialUSA(J)MOUSAMOAIME
Problem Statement
Let and denote three distinct integers, and let denote a polynomial having integer coefficients. Show that it is impossible that P(a) \equal{} b, P(b) \equal{} c, and P(c) \equal{} a.