Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 359.10001
Autor: Eggleton, R.B.; Erdös, Paul; Selfridge, J.L.
Title: The powers that be. (In English)
Source: Am. Math. Mon. 83, 801-805 (1976).
Review: Given a positive integer n and an integer a > 1, the unique integer such that am \leq n < am+1 is called the exponent of a for n. For given n, let En denote the set of (distinct) exponents for n, when we allow a to assume all integers > 1, and similarly let Ep(n) denote the set of exponents for n when we restrict a to only prime values. If m is an exponent for n, let am and bm denote the smallest and largest integer with m as exponent. Similarly let pm and qm denote the smallest and largest prime with exponent m. A number of questions were raised by the authors regarding En, Ep(n), am, bm, pm, qm. Answers or partial answers to some of these questions were given.
Reviewer: S.L.G.Choi
Classif.: * 11A05 Multiplicative structure of the integers
11N05 Distribution of primes
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag