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Topic: Pythagorean triples
Replies: 8   Last Post: Mar 21, 2013 2:53 AM

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Philippe 92

Posts: 44
Registered: 5/10/06
Re: Pythagorean triples
Posted: Jun 26, 2006 9:12 AM
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> Sorry, I should have specified 'an infinite number of
> *non-similar*' triples, where one triple is similar
> to another if each member is multiple of the
> corresponding member.

Where do you see that my formula generates similar triples ?????
They are not, of course !

However, there can't be similar triangles with b=a+1 because a, a+1 are allways coprime !

The list results into :

(3,4,5) (20,21,29) (119,120,169) (696,697,985) ...

just applying the recurrence relation from (0,1,1).

To get direct values without walking through recurrence
relations, we also can use the formula

x(n) = (floor( (1+sqrt(2))(3+2sqrt(2))^n ) - 2 )/4

and for instance the huge triangle for n = 15 :
183648021599, 183648021600, 259717522849
can be obtained directly without calculating the 14 others

Philippe C.

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