This book is mainly devoted to some computational and algorithmic problems in finite fields
such as, for example, polynomial factorization, finding irreducible and primitive polynomials …

P. Turán asked if there exists an absolute constant $ C $ such that for every polynomial $
f\in\mathbb {Z}[x] $ there exists an irreducible polynomial $ g\in\mathbb {Z}[x] $ with $\deg …

On a polynomial conjecture of Pal Turan Page 1 On a polynomial conjecture of Pal Turan
Pradipto Banerjee Department of Mathematics University of South Carolina Columbia, SC …

Many important and interesting problems of mathematics are related to the distribution of
irreducible elements in some special structures. It is well-known that the number of primes in …

We revisit an old problem posed by P. Turán asking whether there exists an absolute
constant C> 0 C>0 such that if f (x)∈ Z xf(x)∈Zx with deg f= d \degf=d, then there is a …

We investigate a variant of Wirsing's problem on approximation to a real number by real
algebraic numbers of degree exactly $ n $. This has been studied by Bugeaud and Teulie …

Let f (x) and g (x) be polynomials in $\mathbb F_ {2}[x] $ with ${\rm deg}\text {} f= n $. It is
shown that for $ n\gg 1$, there is an $ g_ {1}(x)\in\mathbb F_ {2}[x] $ with ${\rm deg}\text {} g …

Michael Filaseta obtained his Ph. D. from the University of Illinois in 1984. He is currently a
professor at the University of South Carolina, South Carolina, USA. He has broad interests in …

An old problem of P. Turán asks if every polynomial with integer coefficients lies close to an
irreducible polynomial of the same degree or less, where the distance between two …

In this paper, we consider a variant of Tur\'an's problem on the distance from an integer
polynomial in $\mathbb {Z}[x] $ to the nea\-rest irreducible polynomial in $\mathbb {Z}[x] …