MathDB

KMO second round #2

Source:

May 6, 2005

algebrapolynomialnumber theoryrelatively primenumber theory unsolved

Problem Statement

x

and

y

are positive and relatively prime and

z

is an integer. They satisfy

(5z-4x)(5z-4y)=25xy

. Show that at least one of

10z+x+y

or quotient of this number divided by

3

is a square number (i.e. prove that

10z+x+y

or integer part of

\frac{10z+x+y}{3}

is a square number).