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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: 2,836 Thanks: 1478 March 19th, 2017, 07:28 AM   #3
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Quote:
 Originally Posted by prashantakerkar Is it possible to find the largest Hypotenuse integer value in Pythagoras theorem? Thanks & Regards, Prashant S Akerkar
No.

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 right-angled 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: 1,310 Thanks: 550 NO March 19th, 2017, 10:12 AM   #6
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Quote:
 Originally Posted by prashantakerkar Is there no way to Compute the largest Hypotenuse integer value in a right-angled triangle? Hypotenuse Examples : 5,10,13 ... etc. Can a computer program help in this regard?
I was under the impression that this member was banned a few months ago for posting ridiculous questions. Is there no way to ban him permanently?
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. Tags hypotenuse, i integer, integer, largest, pythagoras, theorem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post tanz10 Geometry 3 February 18th, 2015 09:57 AM sonu_pal Algebra 2 September 12th, 2010 01:19 PM sonu_pal Algebra 6 September 12th, 2010 12:47 PM rose3 Number Theory 3 March 1st, 2010 06:24 PM Hussam Number Theory 1 December 30th, 2008 06:45 AM

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