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March 19th, 2017, 06:57 AM  #1 
Banned Camp Joined: Aug 2011 Posts: 534 Thanks: 2  Pythagoras theorem  Largest Hypotenuse integer value.
Is it possible to find the largest Hypotenuse integer value in Pythagoras theorem? Thanks & Regards, Prashant S Akerkar Last edited by skipjack; March 19th, 2017 at 04:16 PM. 
March 19th, 2017, 07:27 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,767 Thanks: 1422  
March 19th, 2017, 07:28 AM  #3  
Senior Member Joined: May 2016 From: USA Posts: 1,126 Thanks: 468  Quote:
Consider as an example hypotenuse of $5 = \sqrt{25} = \sqrt{16 + 9} = \sqrt{4^2 + 3^2} \implies$ $5a = a \sqrt{4^2 + 3^2} = \sqrt{(4a)^2 + (3a)^2},\ a \ge 0.$ So $10 = 2 * 5 = \sqrt{100} = \sqrt{64 + 36} = \sqrt{(2 * 4)^2 + (2 * 3)^2}.$ Last edited by skipjack; March 19th, 2017 at 04:16 PM.  
March 19th, 2017, 07:48 AM  #4 
Banned Camp Joined: Aug 2011 Posts: 534 Thanks: 2 
Is there no way to Compute the largest Hypotenuse integer value in a rightangled triangle? Hypotenuse Examples : 5,10,13 ... etc. Can a computer program help in this regard? Thanks & Regards, Prashant S Akerkar Last edited by skipjack; March 19th, 2017 at 04:15 PM. 
March 19th, 2017, 09:15 AM  #5 
Senior Member Joined: May 2016 From: USA Posts: 1,126 Thanks: 468  NO 
March 19th, 2017, 10:12 AM  #6  
Senior Member Joined: May 2008 Posts: 290 Thanks: 76  Beer soaked ramblings follow. Quote:
Can a computer program help in this regard? Thanks & Regards, Sir jonah, the hammered reluctant math knight errant Last edited by skipjack; March 19th, 2017 at 04:16 PM.  

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hypotenuse, i integer, integer, largest, pythagoras, theorem 
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