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Factoring Polynomials with Rational Coefficients.

H.W. jr. Lenstra, A.K. Lenstra, L. Lovász (1982)

Mathematische Annalen

Factorisation in fractional powers

A. J. van der Poorten (1995)

Acta Arithmetica

Factorization of matrices associated with classes of arithmetical functions

Shaofang Hong (2003)

Colloquium Mathematicae

Let f be an arithmetical function. A set S = x₁,..., xₙ of n distinct positive integers is called multiple closed if y ∈ S whenever x|y|lcm(S) for any x ∈ S, where lcm(S) is the least common multiple of all elements in S. We show that for any multiple closed set S and for any divisor chain S (i.e. x₁|...|xₙ), if f is a completely multiplicative function such that (f*μ)(d) is a nonzero integer whenever d|lcm(S), then the matrix $(f (x_{i}, x_{i}))$ having f evaluated at the greatest common divisor $(x_{i}, x_{i})$ of $x_{i}$ and $x_{i}$ as its...

Fermat's Equation in Matrices

Khazanov, Alex (1995)

Serdica Mathematical Journal

The Fermat equation is solved in integral two by two matrices of determinant one as well as in finite order integral three by three matrices.

Fermat's theorem for matrices revisited

Štefan Schwarz (1985)

Mathematica Slovaca

Fifteen problems in number theory.

Pethö, Attila (2010)

Acta Universitatis Sapientiae. Mathematica

Finding integers k for which a given Diophantine equation has no solution in kth powers of integers

Andrew Granville (1992)

Acta Arithmetica

Finding the roots of polynomial equations: an algorithm with linear command.

Bernard Beauzamy (2000)

Revista Matemática Complutense

We show how an old principle, due to Walsh (1922), can be used in order to construct an algorithm which finds the roots of polynomials with complex coefficients. This algorithm uses a linear command. From the very first step, the zero is located inside a disk, so several zeros can be searched at the same time.

Finiteness of a class of Rabinowitsch polynomials

Jan-Christoph Schlage-Puchta (2004)

Archivum Mathematicum

We prove that there are only finitely many positive integers $m$ such that there is some integer $t$ such that $| n^{2} + n - m |$ is 1 or a prime for all $n \in [t + 1, t + \sqrt{m}]$ , thus solving a problem of Byeon and Stark.

Fixpunktmannigfaltigkeiten symplektischer Matrizen

B. Steinle (1972)

Acta Arithmetica

Flat cyclotomic polynomials of order four and higher.

Kaplan, Nathan (2010)

Integers

Fonctions entières à valeurs dans un corps de nombres

Mohammed Ably (2011)

Bulletin de la Société Mathématique de France

Soit $Γ$ un sous-groupe de rang maximal d’un corps de nombres $𝐤$ . On montre qu’une fonction entière, envoyant $Γ$ dans l’anneau des entiers d’une extension finie de $𝐤$ , de croissance analytique et arithmétique faibles est un polynôme. Ce résultat étend un théorème bien connu de Pólya. On montre également que ce résultat est à constante près optimal.

Further generalizations of the Fibonacci-coefficient polynomials.

Mátyás, Ferenc (2008)

Annales Mathematicae et Informaticae

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