The divisor problem for (k, r) — integers

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

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 ...

Sets of Integers and Quasi–integers with Pairwise Common Divisor

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.

INTEGERS WITH A DIVISOR IN (y, 2y]

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 ...