MathDB

infinitely relative prime solutions to a+b+c=u+v and a^2+b^2+c^2=u^2+v^2

Source: Tuymaada 1994 p7

April 27, 2019

algebrasystem of equationsrelatively primeDiophantine Equations

Problem Statement

Prove that there are infinitely many natural numbers

a,b,c,u

and

v

with greatest common divisor

1

satisfying the system of equations:

a+b+c=u+v

and

a^2+b^2+c^2=u^2+v^2