Divisors Of Integers Research Articles

On the distribution of divisors of integers in residue classes (mod k)

We consider the distribution of the divisors of n among the reduced residue classes (mod k), and establish mean-value theorems for the variance of this distribution. A result to the effect that for almost all n < x this distribution is very even, provided k is not too large compared with x, is derived; this is similar to but more precise than a theorem of Erdös, and is thus a new proof of his result.

Approximating the Frequencies of the Musical Scale with Digital Counter Circuits

All 12 frequencies of an even-tempered scale can be approximated by frequency division of the output of a single, stable, high-frequency oscillator. Digital integrated circuits have now become a convenient means for dividing by a different integer for each note. The 12 integer divisors giving the smallest attainable maximum frequency error are tabulated for binary counters ranging from 6–12 stages.

Greatest Common Divisor of Several Integers and an Associated Linear Diophantine Equation

Greatest Common Divisor of Several Integers and an Associated Linear Diophantine Equation

A note on a number theoretical paer of Sierpinski

W. Sierpinski [5] has just published the following theorem: set A of all primes which are divisors of integers of form 2r + l contains all primes of the form 8«+ 3 and infinitely many primes of the form 8« + l. The set B of all primes which are divisors of integers of the form 22s+1 —1 contains all primes of the form 8«+ 7 and some primes of the form 8« + l. Every prime of form 8w + l belongs either to A or to B. The question whether the set B contains infinitely many primes of form 8w + l is raised, but remains open. In this note a simple proof of this result will be given. Moreover, it will be shown that B contains infinitely many primes of form 8« +1. More exactly, we prove a little more.

Note on the Number of Prime Divisors of Integers

Journal of the London Mathematical SocietyVolume s1-12, Issue 4 p. 308-314 Articles Note on the Number of Prime Divisors of Integers Paul Erdös, Paul Erdös The University ManchesterSearch for more papers by this author Paul Erdös, Paul Erdös The University ManchesterSearch for more papers by this author First published: October 1937 https://doi.org/10.1112/jlms/s1-12.48.308Citations: 8AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volumes1-12, Issue4October 1937Pages 308-314 RelatedInformation

Functions of coprime divisors of integers

Functions of coprime divisors of integers

Notes on Greatest Common Divisor and Least Common Multiple of Integers

(1912). Notes on Greatest Common Divisor and Least Common Multiple of Integers. The American Mathematical Monthly: Vol. 19, No. 1, pp. 4-6.

Notes on Greatest Common Divisor and Least Common Multiple of Integers

Notes on Greatest Common Divisor and Least Common Multiple of Integers