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Old 2018-01-08, 09:39   #1
Alberico Lepore
 
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Default 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?
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Old 2018-01-08, 10:20   #2
jnml
 
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Quote:
Originally Posted by Alberico Lepore View Post
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.
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Old 2018-01-08, 10:58   #3
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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
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Old 2018-01-08, 16:21   #4
LaurV
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Quote:
Originally Posted by jnml View Post
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?
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Old 2018-01-08, 16:34   #5
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Quote:
Originally Posted by LaurV View Post
"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.
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Old 2018-01-09, 10:58   #6
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Quote:
Originally Posted by LaurV View Post
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?
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Old 2018-01-09, 14:12   #7
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Quote:
Originally Posted by Alberico Lepore View Post
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).
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Old 2018-01-09, 15:19   #8
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Quote:
Originally Posted by CRGreathouse View Post
b = (4313929 - 12462q - 7q^2)/(32q^2).
what procedure is used to solve it?
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Old 2018-01-09, 15:22   #9
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Quote:
Originally Posted by Alberico Lepore View Post
what procedure is used to solve it?
For example.
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Old 2018-01-09, 15:28   #10
Alberico Lepore
 
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Quote:
Originally Posted by jnml View Post
i do not have PRO
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Old 2018-01-09, 16:26   #11
CRGreathouse
 
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Quote:
Originally Posted by Alberico Lepore View Post
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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