Factoring Polynomials with Rational Coefficients.
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H.W. jr. Lenstra, A.K. Lenstra, L. Lovász (1982)
Mathematische Annalen
A. J. van der Poorten (1995)
Acta Arithmetica
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 having f evaluated at the greatest common divisor of and as its...
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.
Štefan Schwarz (1985)
Mathematica Slovaca
Pethö, Attila (2010)
Acta Universitatis Sapientiae. Mathematica
Andrew Granville (1992)
Acta Arithmetica
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.
Jan-Christoph Schlage-Puchta (2004)
Archivum Mathematicum
We prove that there are only finitely many positive integers such that there is some integer such that is 1 or a prime for all , thus solving a problem of Byeon and Stark.
B. Steinle (1972)
Acta Arithmetica
Kaplan, Nathan (2010)
Integers
Mohammed Ably (2011)
Bulletin de la Société Mathématique de France
Soit un sous-groupe de rang maximal d’un corps de nombres . On montre qu’une fonction entière, envoyant dans l’anneau des entiers d’une extension finie de , 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.
Mátyás, Ferenc (2008)
Annales Mathematicae et Informaticae
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