Yes, that's what I'm saying. Factoring univariate polynomials with integer coefficients (that is, seeing if a polynomial with integer coefficients has smaller

Yes, that's what I'm saying. Factoring univariate polynomials with integer coefficients (that is, seeing if a polynomial with integer coefficients has smaller degree polynomial factors with integer coefficients) is in P [0]. Factoring univariate polynomials over the integers has known to be in P since the 1980s (since LLL came out, which is one of the major reasons why LLL was developed in the first place). Integer factorization is still currently unknown to be in P or not in P. If you see how to use polynomial factoring to factor integers, please let me know. [0] https://en.wikipedia.org/wiki/Factorization_of_polynomials#Factoring_univariate_polynomials_over_the_integers https://en.wikipedia.org/wiki/Factorization_of_polynomials#F...