91Ó°ÊÓ

If the running time of an algorithm is upper constrained by a polynomial expression in the size of the method's input, the algorithm is said to be polynomial time.

Let language is represented as:

$L=\left\{\left(n,a,b\right)|nhasafactorpintherangeaâ\copyright ½pâ\copyright ½b\right\}$$L$is obviously in $NP$, because the factor can act as a certificate. Because it is assuming that $P=NP$, there's a polynomial method that determines the result. Using the method multiple times allows to divide search space.

"Is there a factor in the range $\left(a,a+b/2\right)?$"In this it can represent that there's a factor in the other range if there isn't one.If $k$ is the number of bits in $n$, the total number of times apply the algorithm is $\log n$, or $O\left(k\right)$. As a result, it may isolate one factor with a polynomial number of executions of this technique.