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 2016-07-19, 14:33 #1 bhelmes     Mar 2016 419 Posts pyth. triples and primes A peaceful day for all, There is a relationship between the primitiv Pythagorean triples (a,b,c) with a²+b²=c² resp. the corresponding rational points of the circle with unit 1 (a/c)²+(b/c)²=1 and the group of the complex elements x²+y²=1 mod p where x, y are elements of Np. In addition there is a similar relationship between the primitiv Pythagorean triples resp. the corresponding rational points (c/b)²-(a/b)²=1 resp. (c/a)²-(b/a)²=1 and the group of the complex elements with x²-y²=1 mod p where x, y are elements of Np. These relationships are one explication for the system of primes : http://devalco.de/System/system_one_complex_pyth2.php Perhaps there is somone who likes this explication. Suggestion and improvements are welcome. Nice greetings from the primes Bernhard
2016-07-19, 15:31   #2
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

32·179 Posts

Quote:
 Originally Posted by bhelmes A peaceful day for all, There is a relationship between the primitiv Pythagorean triples (a,b,c) with a²+b²=c² resp. the corresponding rational points of the circle with unit 1 (a/c)²+(b/c)²=1 and the group of the complex elements x²+y²=1 mod p where x, y are elements of Np.
Define your relationship. For which (a,b,c) Pythagorean triple the image will be the (0,1) point on the (unit) circle?

2016-07-20, 10:34   #3
bhelmes

Mar 2016

419 Posts

A peaceful day

Quote:
 Originally Posted by R. Gerbicz Define your relationship. For which (a,b,c) Pythagorean triple the image will be the (0,1) point on the (unit) circle?
I think for (a,b,c) the trivial solution (0,1,1) is a Pythagorean triple
(not very interesting) and the image will be the (0,1) point on the unit circle.

I will add this commentar on the page because it is not clearly expressed.

Nice greetings from the primes
Bernhard

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