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p(a)=b, p(b)=c, p(c)=a not possible for integer cubic (1995 Chile NMO P3)

Source:

November 22, 2021

algebrapolynomialCubic

Problem Statement

p (x) = c_0 + c_1x + c_2x^2 + c_3x^3

is a polynomial with integer coefficients with

a, b,c

integers and different from each other, prove that it cannot happen simultaneously that

p (a) = b

p (b) = c

and

p (c) = a