The deterministic factorization algorithm for polynomials over finite fields that was recently introduced by the author is based on a new type of linearization of the factorization problem. The main ...

We prove that if $f(x)=\sum _{k=0}^{n-1}a_{k}x^{k}$ is a polynomial with no cyclotomic factors whose coefficients satisfy $a_{k}$ ≡ 1 mod 2 for 0 ≤ k < n, then ...

New research details an intriguing new way to solve "unsolvable" algebra problems that go beyond the fourth degree – something that has generally been deemed impossible using traditional methods for ...

Two mathematicians have used a new geometric approach in order to address a very old problem in algebra. In school, we often learn how to multiply out and factor polynomial equations like (x² – 1) or ...

Long considered solved, David Hilbert’s question about seventh-degree polynomials is leading researchers to a new web of mathematical connections. Success is rare in math. Just ask Benson Farb. “The ...