MathDB

{x^2 + Ax + B} and {2x^2 + 2x + C} do not intersect

Source: IMO Shortlist 1995, N2

August 10, 2008

quadraticsmodular arithmeticnumber theorypartitionIMO Shortlist

Problem Statement

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 \equal{} \{x^2 \plus{} Ax \plus{} B : x \in \mathbb{Z}\} and M_2 \equal{} {2x^2 \plus{} 2x \plus{} C : x \in \mathbb{Z}} do not intersect.

Back to Problems View on AoPS