mersenneforum.org 20th Test of primality and factorization of Lepore with Pythagorean triples
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2018-01-08, 09:39   #1
Alberico Lepore

May 2017
ITALY

47510 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?
Attached Files
 20th Test of primality and factorization of Lepore with Pythagorean triples.pdf (27.6 KB, 138 views)

2018-01-08, 10:20   #2
jnml

Feb 2012
Prague, Czech Republ

32·19 Posts

Quote:
 Originally Posted by Alberico Lepore 20th Test of primality and factorization of Lepore with Pythagorean triples (conjecture) in linear coputational complexity What do you think about it?
Copy of the document body:

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.

 2018-01-08, 10:58 #3 Alberico Lepore     May 2017 ITALY 52·19 Posts additionally N^2+C^2=D^2 , (C+D)/q=p^2 , D-C=q and N^2+C^2=D^2 , (C+D)/p=q^2 , D-C=p
2018-01-08, 16:21   #4
LaurV
Romulan Interpreter

Jun 2011
Thailand

2·5·937 Posts

Quote:
 Originally Posted by jnml 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.
Leaving apart the fact that this ignores the time to search in the table, I have a better version:

"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?

2018-01-08, 16:34   #5
CRGreathouse

Aug 2006

32×5×7×19 Posts

Quote:
 Originally Posted by LaurV "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?
I have a method by which I can construct the n-th 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.

2018-01-09, 10:58   #6
Alberico Lepore

May 2017
ITALY

7338 Posts

Quote:
 Originally Posted by LaurV Leaving apart the fact that this ignores the time to search in the table, I have a better version: "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?
Because with the Pythagorean triples I found a method to eliminate a factor.
Only I have to get back to solving this (2077*(4*sqrt(2*b+1)-3))/(32*b+7)=q
can you help me?

2018-01-09, 14:12   #7
CRGreathouse

Aug 2006

32×5×7×19 Posts

Quote:
 Originally Posted by Alberico Lepore Because with the Pythagorean triples I found a method to eliminate a factor. Only I have to get back to solving this (2077*(4*sqrt(2*b+1)-3))/(32*b+7)=q can you help me?
b = (4313929 - 12462q - 7q^2)/(32q^2).

2018-01-09, 15:19   #8
Alberico Lepore

May 2017
ITALY

52·19 Posts

Quote:
 Originally Posted by CRGreathouse b = (4313929 - 12462q - 7q^2)/(32q^2).
what procedure is used to solve it?

2018-01-09, 15:22   #9
jnml

Feb 2012
Prague, Czech Republ

17110 Posts

Quote:
 Originally Posted by Alberico Lepore what procedure is used to solve it?
For example.

2018-01-09, 15:28   #10
Alberico Lepore

May 2017
ITALY

1DB16 Posts

Quote:
 Originally Posted by jnml
i do not have PRO

2018-01-09, 16:26   #11
CRGreathouse

Aug 2006

32×5×7×19 Posts

Quote:
 Originally Posted by Alberico Lepore i do not have PRO
The free version should do it. Failing that, you could just, you know, solve the equation?

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