mersenneforum.org P_1_6 Integer Factorization
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2021-04-25, 19:50   #1
Alberico Lepore

May 2017
ITALY

1E216 Posts
P_1_6 Integer Factorization

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 ?
Attached Files
 P_1_6_integer_factorization.pdf (40.5 KB, 47 views) Method of solving the factorization system of P_1_6 Integer Factorization.pdf (43.7 KB, 28 views)

2021-04-26, 13:54   #2
Alberico Lepore

May 2017
ITALY

7428 Posts

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

Error

Quote:
 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

Quote:
 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 ->

 2021-04-26, 15:32 #3 mathwiz   Mar 2019 9D16 Posts 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.

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