P_1_6 Integer Factorization

[Alberico Lepore]

P_1_6 Integer Factorization

and

Method of solving the factorization system of P_1_6 Integer Factorization (Exercise)


after more than 6 years I think I made it.
what do you think ?

[Alberico Lepore]

unfortunately there is a very important error in the second pdf but the first pdf is correct


Error

We know that two consecutive odd numbers are divisible by 4 while even numbers 2 * even + 4 = 4 * R.

(7*k^2 + 10*k + 186)+2*(8*k+1)=4*R

k*(7*k+26)+188=4*R -> k is even -> k=2*h -> a1 is odd

let's try if a1 was even

(7*k^2 + 10*k + 186)+4*(8*k+1)=4*R

7*k*(k+6)+190 =4*R

k cannot be even or odd

no information ?

We know that two consecutive odd numbers are divisible by 4.

then

2*(28*h^2 + 11*h + 12)+2*(16*h+1)=56*h^2+27*h+26=4*R

-> 4*R=2*(28*h^2+27*h+13) -> h is odd ->

[mathwiz]

You continue throwing large numbers of equations at us and saying "what do you think?"

Show how your method can factor an arbitrary 20-digit semiprime, for example.