AbstractFor any set A of natural numbers let F(x, A) denote the number of natural numbers up to x that are divisible by no element of A and let H(x, K) be the maximum of F(x, A) when A runs over the sets not containing 1 and having a sum of reciprocals not greater than K. A logarithmic asymptotic formula is given for H(x, K)—in particular it shows H(x, K) < xε for K > K0(ε)—and some related problems are discussed
AbstractLet A denote a finite sequence of integers and put Ad = {a ∈ A : a ≡ 0(d)}. Let P denote a s...
In this paper, we report efficient implementations of the linear sieve and the cubic sieve methods f...
We consider Chebyshev polynomials, (Formula presented.), for infinite, compact sets (Formula present...
AbstractFor any set A of natural numbers let F(x, A) denote the number of natural numbers up to x th...
AbstractThe main object of the paper is to prove that if P is a set of primes with sum of reciprocal...
Let k ≥ 2 and ai, bi(1 ≤ i ≤ k) be integers such that ai > 0 and ∏1 ≤ i < j ≤ k (ai bj - aj bi) ≠ 0....
AbstractLet k⩾2 and ai,bi (1⩽i⩽k) be integers such that ai>0 and ∏1⩽i<j⩽k(aibj−ajbi)≠0. Let Ω(m) den...
In this paper one proves that the remaining sequence of Smarandache n-ary sieve contains infinitely ...
Abstract. We are interested in classifying those sets of primes P such that when we sieve out the in...
For each prime p, let Ip⊂Z/pZ denote a collection of residue classes modulo p such that the cardinal...
Let N a,b (x) count the number of primes p = x with p dividing a k + b k for some k = 1. It is known...
The Cubic Sieve Method for solving the Discrete Logarithm Problem in prime fields requires a nontriv...
Abstract For any fixed positive integer k ≥ 2, the power k sieve is defined as following: Starting t...
We present two algorithms for splitting a general composite number, the quadratic sieve algorithm (Q...
Let S be a set of n elements, and let H be a set-system on S, which satisfies that the size of any e...
AbstractLet A denote a finite sequence of integers and put Ad = {a ∈ A : a ≡ 0(d)}. Let P denote a s...
In this paper, we report efficient implementations of the linear sieve and the cubic sieve methods f...
We consider Chebyshev polynomials, (Formula presented.), for infinite, compact sets (Formula present...
AbstractFor any set A of natural numbers let F(x, A) denote the number of natural numbers up to x th...
AbstractThe main object of the paper is to prove that if P is a set of primes with sum of reciprocal...
Let k ≥ 2 and ai, bi(1 ≤ i ≤ k) be integers such that ai > 0 and ∏1 ≤ i < j ≤ k (ai bj - aj bi) ≠ 0....
AbstractLet k⩾2 and ai,bi (1⩽i⩽k) be integers such that ai>0 and ∏1⩽i<j⩽k(aibj−ajbi)≠0. Let Ω(m) den...
In this paper one proves that the remaining sequence of Smarandache n-ary sieve contains infinitely ...
Abstract. We are interested in classifying those sets of primes P such that when we sieve out the in...
For each prime p, let Ip⊂Z/pZ denote a collection of residue classes modulo p such that the cardinal...
Let N a,b (x) count the number of primes p = x with p dividing a k + b k for some k = 1. It is known...
The Cubic Sieve Method for solving the Discrete Logarithm Problem in prime fields requires a nontriv...
Abstract For any fixed positive integer k ≥ 2, the power k sieve is defined as following: Starting t...
We present two algorithms for splitting a general composite number, the quadratic sieve algorithm (Q...
Let S be a set of n elements, and let H be a set-system on S, which satisfies that the size of any e...
AbstractLet A denote a finite sequence of integers and put Ad = {a ∈ A : a ≡ 0(d)}. Let P denote a s...
In this paper, we report efficient implementations of the linear sieve and the cubic sieve methods f...
We consider Chebyshev polynomials, (Formula presented.), for infinite, compact sets (Formula present...
DOI
Add to ORKG