by primework123 » Sat Nov 07, 2015 11:10 am
Hey primework123, I like your previous post.
Suppose, we are given a positive integer, n, which is the product of two large primes, p and q, how do you factor n?
In base-10, we can let p = [tex]\sum_{i=0}^{j}a_{i}*10^{i}[/tex], and q = [tex]\sum_{i=0}^{k}b_{i}*10^{i}[/tex] where
[tex]a_{i}, b_{i}\in Z_{10 }[/tex]={0,1,2,3,4,5,6,7,8,9}. Furthermore, we assume [tex]500\le j \le k[/tex], and [tex]p \ne q[/tex].[/quote][/quote]
So, n = [tex]\sum_{i=0}^{l}r_{i}*10^{i}[/tex] where [tex]r_{0} \in[/tex] {1, 3, 7, 9}.[/quote]
primework123,
So, given n as a product two large, unknown, and distinct prime numbers, p and q, we need to solve a
system of equations to find
[tex]a_{i}[/tex] and [tex]b_{i}[/tex] for all i, [tex]0 \le i \le j[/tex] and [tex]0 \le i \le k[/tex], respectively, in order to construct the unknown prime factors, p and q.
But, how do
optimization and
handshaking helps us to solve the system of equations efficiently (in polynomial time or less)?
_________________________________________
Hi,
Yes, you're on the right path to a solution which was discovered back in the fall of 2010. Keep up the good work, and you'll sure to find the proper solution. I have given enough hints...
Best wishes,
David Cole
(aka primework123)
Keep the faith (effort and hope) and keep an open mind.
http://biblia.com/verseoftheday/image/Ro8.28
Hey primework123, I like your previous post.
Suppose, we are given a positive integer, n, which is the product of two large primes, p and q, how do you factor n?
In base-10, we can let p = [tex]\sum_{i=0}^{j}a_{i}*10^{i}[/tex], and q = [tex]\sum_{i=0}^{k}b_{i}*10^{i}[/tex] where
[tex]a_{i}, b_{i}\in Z_{10 }[/tex]={0,1,2,3,4,5,6,7,8,9}. Furthermore, we assume [tex]500\le j \le k[/tex], and [tex]p \ne q[/tex].[/quote][/quote]
So, n = [tex]\sum_{i=0}^{l}r_{i}*10^{i}[/tex] where [tex]r_{0} \in[/tex] {1, 3, 7, 9}.[/quote]
primework123,
So, given n as a product two large, unknown, and distinct prime numbers, p and q, we need to solve a [b][u]system of equations[/u][/b] to find
[tex]a_{i}[/tex] and [tex]b_{i}[/tex] for all i, [tex]0 \le i \le j[/tex] and [tex]0 \le i \le k[/tex], respectively, in order to construct the unknown prime factors, p and q.
But, how do [u][b]optimization[/b][/u] and [u][b]handshaking[/b][/u] helps us to solve the system of equations efficiently (in polynomial time or less)?
_________________________________________
Hi,
Yes, you're on the right path to a solution which was discovered back in the fall of 2010. Keep up the good work, and you'll sure to find the proper solution. I have given enough hints...
Best wishes,
David Cole
(aka primework123)
Keep the faith (effort and hope) and keep an open mind. :)
http://biblia.com/verseoftheday/image/Ro8.28