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Polynomial with integer coefficients!

Source: India TST 2001 Day 4 Problem 1

January 31, 2015
algebrapolynomialcomplex numbersnumber theory proposednumber theory

Problem Statement

Complex numbers α\alpha , β\beta , γ\gamma have the property that αk+βk+γk\alpha^k +\beta^k +\gamma^k is an integer for every natural number kk. Prove that the polynomial (x−α)(x−β)(x−γ)(x-\alpha)(x-\beta )(x-\gamma ) has integer coefficients.
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