On the greatest prime factor of a quadratic polynomial

• DOI: 10.1007/bf02395047
• Publication Date: 2006-05-11T17:09:53Z
• Authors: Christopher Hooley

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