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 the problem proposed by Kuhn on the presence of a monotonicity property related to the Kuhn's algorithm for finding roots of a polynomial is solved in the affirmative. Furthermore, an ...

Some new results for finding all convenient moduli $m$ for a complex number-theoretic transform with given transform length $n$ and given primitive $n$th root of unity modulo $m$ are presented.