MathDB

Romanian National Olympiad 2018 - Grade 9 - problem 3

Source: Romania NMO - 2018

April 12, 2018

quadratics

Problem Statement

Let

f,g : \mathbb{R} \to \mathbb{R}

be two quadratics such that, for any real number

r,

f(r)

is an integer, then

g(r)

is also an integer. Prove that there are two integers

m

and

n

such that

g(x)=mf(x)+n, \: \forall x \in \mathbb{R}