20180108, 09:39  #1 
May 2017
ITALY
184_{16} Posts 
20th Test of primality and factorization of Lepore with Pythagorean triples
20th Test of primality and factorization of Lepore with Pythagorean triples
(conjecture) in linear coputational complexity What do you think about it? 
20180108, 10:20  #2  
Feb 2012
Prague, Czech Republ
7·23 Posts 
Quote:
Sian N = p * q with p and q integer then there will be a Pythagorean triplet, with a smaller cateto N and the other two sides C and D (respectively cateto and hypotenuse),such that GCD (N, C, D) = p or GCD (N, C, D) = q. Therefore, having a table with the Pythagorean triples ordered by a minor cateto will be able to factor or establish primality in linear computational complexity. 

20180108, 10:58  #3 
May 2017
ITALY
2^{2}·97 Posts 
additionally
N^2+C^2=D^2 , (C+D)/q=p^2 , DC=q and N^2+C^2=D^2 , (C+D)/p=q^2 , DC=p 
20180108, 16:21  #4  
Romulan Interpreter
Jun 2011
Thailand
2^{3}·29·37 Posts 
Quote:
"Having a table with Natural Numbers N ordered by N, and their factorization will be able to factor or establish primality in linear computational complexity". Why do you need Pythagorean triples? 

20180108, 16:34  #5 
Aug 2006
2·3·977 Posts 
I have a method by which I can construct the nth natural number directly, obviating the need for initialization and storage. Combining our technologies, we could get nearly the efficiency of trial division with just as little memory.

20180109, 10:58  #6  
May 2017
ITALY
2^{2}·97 Posts 
Quote:
Only I have to get back to solving this (2077*(4*sqrt(2*b+1)3))/(32*b+7)=q can you help me? 

20180109, 14:12  #7 
Aug 2006
5862_{10} Posts 

20180109, 15:19  #8 
May 2017
ITALY
604_{8} Posts 

20180109, 15:22  #9 
Feb 2012
Prague, Czech Republ
7×23 Posts 

20180109, 15:28  #10  
May 2017
ITALY
388_{10} Posts 
Quote:


20180109, 16:26  #11 
Aug 2006
5862_{10} Posts 

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