MathDB

Inequality with the gcd of the integers x,y,z

Source: Baltic Way 2007

November 30, 2010

inequalitiesnumber theorygreatest common divisornumber theory proposed

Problem Statement

Let

x,y,z

be positive integers such that

\frac{x+1}{y}+\frac{y+1}{z}+\frac{z+1}{x}

is an integer. Let

d

be the greatest common divisor of

x,y

and

z

. Prove that

d\le \sqrt[3]{xy+yz+zx}