MathDB

0 <= mu + nv <= 2 \sqrt{X}

Source: 2016 Latvia BW TST P2

December 17, 2022

number theoryinequalitiesalgebra

Problem Statement

Given natural numbers

m, n

and

X

such that

X \ge m

and

X \ge n

. Prove that one can find two integers

u

and

v

such that

|u| + |v| > 0

,

|u| \le \sqrt{X}

,

|v| \le \sqrt{X}

and

0 \le mu + nv \le 2 \sqrt{X}.

Back to Problems View on AoPS