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Guest Message by DevFuse

# Pythagorean Triples

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Posted 19 July 2013 - 05:46 PM

The most famous Pythagorean Triangle (a right triangle with all integer sides) is the 3 , 4 , 5 where 3^2 + 4^2 = 5^2. The 'legs', a=3 and b=4, are
consecutive integers, making a nearly-isosceles right triangle. What are the next two smallest integral right triangles with consecutive legs?

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### #2 k-man

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Posted 19 July 2013 - 07:16 PM   Best Answer

Spoiler for

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### #3 bonanova

bonanova

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Posted 19 July 2013 - 08:31 PM

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Vidi vici veni.

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Posted 19 July 2013 - 08:53 PM

Hmm do they consider the hypotenuse a leg in America?
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### #5 superprismatic

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Not just Prismatic

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Posted 19 July 2013 - 08:53 PM

I've exhausted all triangles whose two legs differ by 1 where
the length of the shortest leg is less than or equal to 1010.
I found only 9:
3 4 5
20 21 29
119 120 169
696 697 985
4059 4060 5741
23660 23661 33461
137903 137904 195025
803760 803761 1136689
4684659 4684660 6625109
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### #6 bonanova

bonanova

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Posted 20 July 2013 - 04:48 AM

Hmm do they consider the hypotenuse a leg in America?

No, they don't.

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Vidi vici veni.

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Posted 20 July 2013 - 05:22 AM

Spoiler for further proof

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