Some theorems on the Euler $\phi$-function
نویسندگان
چکیده
منابع مشابه
Arithmetic Functions and the Euler Phi Function
• An arithmetic function takes positive integers as inputs and produces real or complex numbers as outputs. • If f is an arithmetic function, the divisor sum Df(n) is the sum of the values of f at the positive divisors of n. • τ (n) is the number of positive divisors of n; σ(n) is the sum of the positive divisors of n. • The Möbius function μ(n) is 1 if n = 1 and 0 if n has a repeated prime fac...
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which give the arithmetic and the geometric means of the first n values of the Euler function, respectively, are uniformly distributed modulo 1. A. Schinzel modified these questions by asking whether these sequences are dense modulo 1. This question was repeated at the meeting on Uniform Distribution in Luminy in January 2008. In this paper, we give an affirmative answer to Schinzel’s question....
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Let φ(·) denote the Euler function, and let a > 1 be a fixed integer. We study several divisibility conditions which exhibit typographical similarity with the standard formulation of the Euler theorem, such as an ≡ 1 (mod φ(n)), and we estimate the number of positive integers n ≤ x satisfying these conditions. 2000 Mathematics Subject Classification. 11A07, 11N37.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1943
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1943-07898-6