Pythagorean triples? 3-4-5, and 5-12-13

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December 17th 2012, 10:25 PM
asilvester635

Pythagorean triples? 3-4-5, and 5-12-13

can anyone explain this concept to me?
December 17th 2012, 10:29 PM
jakncoke

Re: Pythagorean triples? 3-4-5, and 5-12-13

Basically, a pythogorean triple is just 3 positive integers which satisfy the pythogorean theorem $a^2 + b^2 = c^2$ .
So $3^2 + 4^2 = 5^2 \text{ and } 5^2 + 12^2 = 13^2$
December 17th 2012, 10:35 PM
MarkFL

Re: Pythagorean triples? 3-4-5, and 5-12-13

In a nutshell, a Pythagorean triple $(a,b,c)$ has the property that $a^2+b^2=c^2$

Perhaps the best know method for generating such triples (attributed to Euclid) is to let:

$a=m^2-n^2$

$b=2mn$

$c=m^2+n^2$

where $n<m$ and $m,n\in\mathbb{N}$ .

A triple is said to be primitive if $a,b,c$ are co-prime, and requires $m,n$ to be co-prime and $m-n$ is odd.

Pythagorean triple - Wikipedia, the free encyclopedia

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