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March 13th, 2014, 09:48 AM  #1 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039  Special right triangle.
Had fun with this one: Pythagorean right triangle ABC, sides a, b and c (a < b < c). a = u^2 + u b = v^2 + v c = w^2 + w Find smallest case. I'll post the answer in a week if nobody finds it... 
March 13th, 2014, 09:54 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: Special right triangle.
Are a, b and c positive integers?

March 13th, 2014, 10:38 AM  #3  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039  Re: Special right triangle. Quote:
Go have your 2nd coffee :P  
March 13th, 2014, 01:36 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,036 Thanks: 2273 
(a, b, c) = (17556, 20592, 27060)

March 13th, 2014, 05:19 PM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039  Re: Special right triangle.
Yep. Thanks for confirming, Skip. I went up to a (shortest side) = 5 million; couldn't find any more. Of course, all sides have to be even. 

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