Bachet's Theorem

Date: 10/08/98 at 14:45:55
From: Jonathan
Subject: 4 square numbers make any other?

Hi!

In maths lesson today my maths teacher said that a mathematician 
discovered that you can make any number by adding together a 
combination of no more than 4 square numbers. He said he couldn't 
remember the name of the mathematician with that theory. I was 
wondering if you knew his name.  I have just started Secondary 
School, and I think my teacher would be very impressed if I found out!
Thank you,

- Jonathan, England

Date: 10/08/98 at 15:03:04
From: Doctor Rob
Subject: Re: 4 square numbers make any other?

This fact is called "Bachet's Theorem."  It has been claimed that this 
was known to Diophantus, the ancient Greek, and it was stated 
explicitly by Bachet in 1621, but was first proven by Joseph-Louis 
Lagrange in 1770. For his biography, consult this page from the 
MacTutor Math History Archive site at St. Andrews, and follow the link 
for Lagrange:
  
  http://www-history.mcs.st-and.ac.uk/history/Indexes/L.html   

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/