20180108, 09:39  #1 
May 2017
ITALY
2×3^{2}×29 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
2×3^{2}×11 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
522_{10} 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
"name field"
Jun 2011
Thailand
3·5·683 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
5,987 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
2·3^{2}·29 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
5,987 Posts 

20180109, 15:19  #8 
May 2017
ITALY
2·3^{2}·29 Posts 

20180109, 15:22  #9 
Feb 2012
Prague, Czech Republ
2×3^{2}×11 Posts 

20180109, 15:28  #10  
May 2017
ITALY
1012_{8} Posts 
Quote:


20180109, 16:26  #11 
Aug 2006
5,987 Posts 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
18th Test of primality and factorization of Lepore in 5 * log_25 (N) (New Year's algorithm)  Alberico Lepore  Alberico Lepore  2  20180101 21:31 
14° Primality test and factorization of Lepore ( conjecture )  Alberico Lepore  Alberico Lepore  48  20171230 09:43 
Final Lucas Lehmer residuals and Pythagorean triples  a nicol  Miscellaneous Math  21  20171219 11:34 
Pythagorean triples  Rokas  Math  3  20050102 03:50 
Pythagorean Triples  jinydu  Puzzles  6  20031213 10:10 