 mersenneforum.org Phantom factorization - subcubic factorization of integers?
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Alberico Lepore

May 2017
ITALY

3×5×31 Posts Phantom factorization - subcubic factorization of integers?

There are 48 systems in the paper "phantom factorization" .

Will the combination of three of them lead to factorization?

Here is an example of a combination of three times the first system
(but it is better to use three different systems)

N=187 , x=w=g=3 , u=1 , v=7 ,h=9

N^2*x*(x+2+4*u)=[8*((96 k² + 24 k + 1)-3*a*(a-1)/2)+1]/3
,
sqrt[(8*(96 k² + 24 k + 1)+1)/3+1]-(2*a-1)=[2*(3*b+1-(b-a+1))+1-(4*a-2)]=x*[2*(3*z+1-(z-y+1))+1]^2
,
sqrt[(8*(96 k² + 24 k + 1)+1)/3+1]+(2*a-1)=[2*(3*b+1-(b-a+1))+1]=(x+2+4*u)*[2*(3*z+1-(z-y+1))+1-(4*y-2)]^2
,
(96 k² + 24 k + 1-1)/3=2*b*(b+1)
,
N^2*w*(w+2+4*v)=[8*((96 m² + 24 m + 1)-3*c*(c-1)/2)+1]/3
,
sqrt[(8*(96 m² + 24 m + 1)+1)/3+1]-(2*c-1)=[2*(3*d+1-(d-c+1))+1-(4*c-2)]=w*[2*(3*z+1-(z-y+1))+1]^2
,
sqrt[(8*(96 m² + 24 m + 1)+1)/3+1]+(2*c-1)=[2*(3*d+1-(d-c+1))+1]=(w+2+4*v)*[2*(3*z+1-(z-y+1))+1-(4*y-2)]^2
,
(96 m² + 24 m + 1-1)/3=2*d*(d+1)
,
N^2*g*(g+2+4*h)=[8*((96 n² + 24 n + 1)-3*f*(f-1)/2)+1]/3
,
sqrt[(8*(96 n² + 24 n + 1)+1)/3+1]-(2*f-1)=[2*(3*r+1-(r-f+1))+1-(4*f-2)]=g*[2*(3*z+1-(z-y+1))+1]^2
,
sqrt[(8*(96 n² + 24 n + 1)+1)/3+1]+(2*f-1)=[2*(3*r+1-(r-f+1))+1]=(g+2+4*h)*[2*(3*z+1-(z-y+1))+1-(4*y-2)]^2
,
(96 n² + 24 n + 1-1)/3=2*r*(r+1)
,
(3*N-1)/8=3*z*(z+1)/2-3*y*(y-1)/2+(3*z+1)*(3*z+2)/2

Since I don't have CAS and I don't know how to use them I'm not sure, could someone tell me, please, if the system of the three systems is resolved?

This is a free copy of https://www.academia.edu/43115308/Phantom_factorization for MersenneForum Friend
Attached Files phantom factorization.pdf (46.2 KB, 32 views)   2020-05-27, 12:20 #2 mathwiz   Mar 2019 22×52 Posts I'd be amazed if anybody on the forum has the patience to put up with your gibberish anymore, after you've been told repeatedly to test your own equations.  Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post Alberico Lepore Alberico Lepore 30 2020-02-27 09:53 Robert Holmes Factoring 19 2010-11-08 18:46 kurtulmehtap Math 25 2010-09-12 14:13 dleclair NFSNET Discussion 1 2006-03-21 05:11 Wacky NFSNET Discussion 1 2006-03-20 23:43

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