My Math Forum Pythagoras theorem - Largest Hypotenuse integer value.

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 March 19th, 2017, 06:57 AM #1 Senior Member   Joined: Aug 2011 Posts: 478 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: 2,508 Thanks: 1234
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 Senior Member   Joined: Aug 2011 Posts: 478 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: 591 Thanks: 251 NO
March 19th, 2017, 10:12 AM   #6
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Beer soaked ramblings follow.
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

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