MathDB

y =\sqrt{x^2 +a} has infinite solutions with rational coordinates

Source: 1997 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p2

January 27, 2020

rationalnumber theoryanalytic geometry

Problem Statement

Show that for any rational number

a

the equation

y =\sqrt{x^2 +a}

has infinitely many solutions in rational numbers

x

and

y