Over the centuries, mathematicians have developed a variety of methods of solving equations. Using the capabilities of modern computers, they have explored in detail how these age-old recipes ...

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Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another. The equation x 2 – 5 = 0 is a bit trickier. The polynomial can’t be ...

Algorithms for polynomial computation over finite fields form a crucial domain in computational mathematics, with extensive applications ranging from cryptography and ...

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them. Problems in ...

In this article we consider matrix factorizations of a polynomial where the two matrices appearing in the factorization are the same, which we call "matrix square roots." The main result is that any ...