[Search for users] [Overall Top Noters] [List of all Conferences] [Download this site]

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

1794.0. "Crux Mathematicorum 1865" by RUSURE::EDP (Always mount a scratch monkey.) Mon Sep 20 1993 18:08

    Proposed by Christopher J. Bradley, Clifton College, Bristol, U.K.
    
    Find an integer-sided right-angled triangle with sides x^2-1, y^2-1,
    z^2-1 where x, y, z are integers.

T.R Title User Personal
Name Date Lines

1794.1 CFSCTC::GILBERT Tue Sep 21 1993 01:02 11

T.R	Title	User	Personal Name	Date	Lines
1794.1		CFSCTC::GILBERT		`Tue Sep 21 1993 01:02`	11
	> Find an integer-sided right-angled triangle with sides x^2-1, y^2-1, > z^2-1 where x, y, z are integers. For example: (x,y,z) = (10,13,14), (x^2-1,y^2-1,z^2-1) = (99,168,195), and 99^2 + 168^2 = 38025 = 195^2 Or: (x,y,z) = (265,287,329), (x^2-1,y^2-1,z^2-1) = (70224,82368,108240), and 70224^2 + 82368^2 = 11715897600 = 108240^2

>    Find an integer-sided right-angled triangle with sides x^2-1, y^2-1,
>    z^2-1 where x, y, z are integers.

For example:
	(x,y,z) = (10,13,14),
	(x^2-1,y^2-1,z^2-1) = (99,168,195), and
	99^2 + 168^2 = 38025 = 195^2
Or:
	(x,y,z) = (265,287,329),
	(x^2-1,y^2-1,z^2-1) = (70224,82368,108240), and
	70224^2 + 82368^2 = 11715897600 = 108240^2