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 paper we present the implementation of simultaneous method for the determination of polynomial roots on a distributed memory multicomputer. The total cost of such a parallelization per ...

This is a preview. Log in through your library . Abstract The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the ...

If \((x \pm h)\) is a factor of a polynomial, then the remainder will be zero. Conversely, if the remainder is zero, then \((x \pm h)\) is a factor. Often ...