MathDB

Addition respects rationality in polynomials

Source: RMM Shortlist 2023 A1

February 29, 2024

Polynomialsalgebrarational numberRMM Shortlistpolynomial

Problem Statement

Determine all polynomials

P

with real coefficients satisfying the following condition: whenever

x

and

y

are real numbers such that

P(x)

and

P(y)

are both rational, so is

P(x + y)