IMO Shortlist 1995 problem NC2
Dodao/la:
arhiva2. travnja 2012. Let

denote the set of all integers. Prove that for any integers

and

one can find an integer

for which

and

do not intersect.
%V0
Let $\mathbb{Z}$ denote the set of all integers. Prove that for any integers $A$ and $B,$ one can find an integer $C$ for which $M_1 = \{x^2 + Ax + B : x \in \mathbb{Z}\}$ and $M_2 = {2x^2 + 2x + C : x \in \mathbb{Z}}$ do not intersect.
Izvor: Međunarodna matematička olimpijada, shortlist 1995