
Re: Pythagorean triples
Posted:
Jun 26, 2006 8:11 AM


> There are some Pythagorean triples ( = integers > {a,b,c}: a^2+b^2c^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

