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P(a) integer implies a integer

Source: Singapore MO 2011open round 2 Q4

July 2, 2011
algebrapolynomialcalculusnumber theory proposednumber theory

Problem Statement

Find all polynomials P(x)P(x) with real coefficients such that P(a)∈Z   implies that   a∈Z.P(a)\in\mathbb{Z}\ \ \ \text{implies that}\ \ \ a\in\mathbb{Z}.
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