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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

361.0. "Sum of 3 4th powers a square" by TOOLS::STAN () Sun Oct 20 1985 17:44

Guy, (in Unsolved Problems in Number Thoery, 1981) stated that there
were no known solutions to the diophantine equation

         4    4    4    2
	a  + b  + c  = d   .

I ran a quick program and quite easily found the solution

          4     4     4      2
        12  + 15  + 20  = 481   .


			         4    4    4    4
The diophantine equation	a  + b  + c  = d     remains unsolved.

T.R Title User Personal
Name Date Lines

361.1 TOOLS::STAN Mon Oct 21 1985 15:47 14

T.R	Title	User	Personal Name	Date	Lines
361.1		TOOLS::STAN		`Mon Oct 21 1985 15:47`	14
	It must have been a misprint in Guy's book, because Dickson says the problem was solved by Diophantus, and my solution was known in the 19th century. He also gives a parametric solution: 4 4 4 4 2 2 2 (yz) + (yw) + (zw) = (w - y z ) 2 2 2 where w = y + z . 4 4 4 2 Letting y=3, z=4, w=5, gives 12 + 15 + 20 = 481 .

It must have been a misprint in Guy's book, because Dickson
says the problem was solved by Diophantus, and my solution
was known in the 19th century.  He also gives a parametric
solution:

            4       4       4     4    2 2 2
	(yz)  + (yw)  + (zw)  = (w  - y z )


         2    2    2
where   w  = y  + z  .

			       4     4     4      2
Letting y=3, z=4, w=5, gives 12  + 15  + 20  = 481   .