Schinzel, Andrzej On two theorems of Gelfond and some of their applications. (English) Zbl 0159.07101 Acta Arith. 13, 177-236 (1967). Reviewer: Alan Baker Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 29 Documents MSC: 11J86 Linear forms in logarithms; Baker’s method 11B37 Recurrences 11D61 Exponential Diophantine equations Keywords:measure of irrationality; p-adic measure of irrationality; ratio of two logarithms of algebraic numbers; linear recurrences; exponential Diophantine equations; greatest prime factor of polynomials in integers Citations:Zbl 0161.05201 PDFBibTeX XMLCite \textit{A. Schinzel}, Acta Arith. 13, 177--236 (1967; Zbl 0159.07101) Full Text: DOI EuDML Online Encyclopedia of Integer Sequences: Largest prime factor of n^2 + 1. a(n) is the largest prime divisor of n(n+1). Largest prime divisor of n^2 - 1. Numbers n such that n^2 + 1 is 13-smooth. Number of integers x such that the greatest prime factor of x^2 + 1 is at most A002313(n), the n-th prime not congruent to 3 mod 4. Numbers n such that n^2 + 1 is 100-smooth