MathDB
P(0)^{2},P(1)^{2},P(2)^{2} are integers in a quadratic polynomial

Source: CRMO 2015 region 4 (Karnataka) p2

September 30, 2018
polynomialIntegersquadratic trinomialalgebra

Problem Statement

Let P(x)=x2+ax+bP(x)=x^{2}+ax+b be a quadratic polynomial where aa is real and b≠2b \neq 2, is rational. Suppose P(0)2,P(1)2,P(2)2P(0)^{2},P(1)^{2},P(2)^{2} are integers, prove that aa and bb are integers.
Back to ProblemsView on AoPS