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Publication . Article . Other literature type . 1967

On the greatest prime factor of a quadratic polynomial

Christopher Hooley;
Open Access
Published: 01 Jan 1967 Journal: Acta Mathematica, volume 117, pages 281-299 (issn: 0001-5962, Copyright policy )
Publisher: International Press of Boston

as x ~ ~ , for which as for many other interesting results in the theory of numbers we are indebted to Chebyshev, has a t t racted the interest of several mathematicians. Revealed posthumously as little more than a fragment in one of Chebyshev's manuscripts, the theorem was first published and fully proved in a memoir by Markov in 1895 [6], while later in the same year a generalisation by Ivanov [4] appeared in which the polynomial n2§ 1 was replaced by n2+A for any positive A (an account of both Markov's and Ivanov ' s work is to be found in Paragraphs 147 and 149 of Landau's Primzahlen [5]). In 1921 Nagell [7] improved and further generalised Chebyshev's theorem by shewing that for any e log~ x, X

Subjects by Vocabulary

Microsoft Academic Graph classification: Mathematics Polynomial Prime power Prime factor Combinatorics Square-free polynomial Euler's criterion symbols.namesake symbols Legendre symbol Number theory Degree of a polynomial


General Mathematics

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Acta Mathematica
Article . 1967
License: implied-oa