Sets of integers and quasi-integers with pairwise common divisor

Sets of Integers and Quasi–integers with Pairwise Common Divisor

Sets of Integers with Pairwise Common Divisor and a Factor from a Specified Set of Primes

Integers with a Divisor In

In this note we prove only the important special case (1.1), omitting the parts of the argument required for other cases. In addition, we present an alternate proof, dating from 2002, of the lower bound implicit in (1.1). This proof avoids the use of results about uniform order statistics required in [3], and instead utilizes the cycle lemma from combinatorics. Although shorter and technically ...

Divisor Problems in Special Sets of Positive Integers

Articles by Mercier and the author [10, 11] discuss the situation that S1, S2 are the images of N under certain (monotonic) polynomial functions p1, p2 with integer coefficients. In the present paper, we will consider (in fact in a more general context) the case that one or both of S1, S2 is equal to the set B = BQ(i) consisting of those natural numbers which can be written as a sum of two inte...

Integers with a Large Smooth Divisor

We study the function Θ(x, y, z) that counts the number of positive integers n ≤ x which have a divisor d > z with the property that p ≤ y for every prime p dividing d. We also indicate some cryptographic applications of our results.