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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 8:11 AM
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> There are some Pythagorean triples ( = integers
> {a,b,c}: a^2+b^2-c^2=0) such that the shorter two
> sides differ by only 1. E.g. 20, 21, 29
> ...
> Show that there is an infinite number.


Hi,

Proove that if (a, a+1, c) is a solution
then (3a+2c+1, 3a+2c+2, 4a+3c+2) is a bigger solution
(easy)

Harder : proove that *all* solutions are given by above
recurence relation, from (0,1,1).
(equivallent to : from where does above relation comes ??? )

Regards.
--
Philippe 92
chephip@free.fr



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