Authors: Yuly Shipilevsky
We develop two different polynomial-time integer factorization algorithms. We reduce integer factorization problem to equivalent problem of minimizing a quadratic polynomial with integer coefficients over the integer points in a quadratically constrained two-dimensional region. Next, we reduce those minimization problem to the polynomial-time minimizing a quadratic polynomial with integer coefficients over the integer points in a special two-dimensional rational polyhedron. Next, we reduce integer factorization problem to the problem of enumeration of vertices of integer hull of a special two-dimensional rational polyhedron, solvable in time polynomial by Hartmann's algorithm. Finally, as we show that there exists an NP-hard minimization problem, equivalent to the original minimization problem, we conclude that P = NP.
Comments: 20 Pages.
[v1] 2018-09-10 17:59:12
Unique-IP document downloads: 164 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.