منابع مشابه
Prime divisors of palindromes
Abstract In this paper, we study some divisibility properties of palindromic numbers in a fixed base g ≥ 2. In particular, if PL denotes the set of palindromes with precisely L digits, we show that for any sufficiently large value of L there exists a palindrome n ∈ PL with at least (log log n)1+o(1) distinct prime divisors, and there exists a palindrome n ∈ PL with a prime factor of size at lea...
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We study the values of arithmetic functions taken on the elements of a non-homogeneous Beatty sequence αn+ β , n= 1,2, . . . , where α,β ∈R, and α > 0 is irrational. For example, we show that ∑ n N ω ( αn+ β )∼N log logN and ∑ n N (−1)Ω( αn+β ) = o(N), where Ω(k) and ω(k) denote the number of prime divisors of an integer k = 0 counted with and without multiplicities, respectively. © 2006 Elsevi...
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The initial motivation of the present paper is the following problem of Erd6s and Woods, whose solution would be of interest in logic (see [3, 6, 11, 10, 16]): Does there exist an integer k >=2 with the following property : i f x and y are positive integers such that for l<=i<=k, the two numbers x+ i and y+i have the same prime factors, then x=y. For each integer n->2, let us denote by Supp (n)...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1987
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1987-0908637-1