MathDB

\sqrt x +\sqrt y +\sqrt z=1, \sqrt{x+n} +\sqrt{y+n} +\sqrt{z+n} is an integer

Source: Rioplatense Olympiad 2016 level 3 P2

September 5, 2018

number theoryalgebrasystem of equations

Problem Statement

Determine all positive integers

n

for which there are positive real numbers

x,y

and

z

such that

\sqrt x +\sqrt y +\sqrt z=1

and

\sqrt{x+n} +\sqrt{y+n} +\sqrt{z+n}

is an integer.