The following thread is on the challenging problem of how to quickly factor a composite integer using polynomials.
I wish for other users to answer the question I make in each post, however if it goes unanswered, I'll post it myself eventually (assuming I have it) and then move on to the next part. Furthermore, I'll point out those problems which I feel are ''research questions'' that have currently gone unanswered in the literature.
Consider a degree polynomial and suppose is a composite integer we wish to factor.
Let and .
Argue that if then the product
, is such that