Prime and coprime values of polynomials
نویسندگان
چکیده
منابع مشابه
Prime Values of Polynomials and Irreducibility Testing
In 1857 Bouniakowsky [6] made a conjecture concerning prime values of polynomials that would, for instance, imply that x + 1 is prime for infinitely many integers x. Let ƒ (x) be a polynomial with integer coefficients and define the fixed divisor of ƒ, written d(ƒ), as the largest integer d such that d divides f(x) for all integers x. Bouniakowsky conjectured that if f(x) is nonconstant and irr...
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1 Supported by National Natural Science Foundation of China, Grant No. 0171046 and the “ 333 Project” Foundation of Jiangsu Province of China. The work was done while first author was visiting the Mathematical Institute of the Hungarian Academy of Sciences. 2 Supported by Hungarian National Foundation for Scientific Research, Grants No. F 026049 and T 30074 3 Supported by Hungarian National Fou...
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Let /(x) be a polynomial with integer coefficients, and let D(/)-gx.d.{/.(*):*eZ}. It was conjectured by Bouniakowsky in 1857 that if f(x) is nonconstant and irreducible over Z, theii \f(x)\/D(f) is prime for infinitely many integers x. It is shown that there exist irreducible polynomials f(x) with D(f) = 1 such that the smallest integer x for which \f(x)\ is prime is large as a function of the...
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A coprime labeling of a simple graph of order n is a labeling in which adjacent vertices are given relatively prime labels, and a graph is prime if the labels used can be taken to be the first n positive integers. In this paper, we consider when ladder graphs are prime and when the corresponding labeling may be done in a cyclic manner around the vertices of the ladder. Furthermore, we discuss c...
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ژورنال
عنوان ژورنال: L’Enseignement Mathématique
سال: 2020
ISSN: 0013-8584
DOI: 10.4171/lem/66-1/2-9