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
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