
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 4th, 2017, 06:14 AM  #1 
Newbie Joined: Oct 2017 From: sweden Posts: 19 Thanks: 0  Some problems in elementary arithmetic functions
Hello, I ran in to this problem and I cant seem to show this although it seems intuitively correct: Given any positive integer $n>1$, prove that there are infinitely many integers $x$ satisfying $d(x)=n$. Where $d(n)$ is the number of positive divisors of $n$. I will appreciate the help. 
November 4th, 2017, 07:57 AM  #2 
Senior Member Joined: May 2016 From: USA Posts: 922 Thanks: 368 
Consider the set of integers that consists of all primes raised to the first power. How many distinct divisors does each number in that set contain? How many numbers does that set contain? Now consider the set of integers that consists of all primes raised to the second power. How many distinct divisors does each number in that set contain? How many numbers does that set contain? Can you build a proof by induction from those clues? 
November 11th, 2017, 09:00 PM  #3 
Newbie Joined: Oct 2017 From: sweden Posts: 19 Thanks: 0 
That was very helpful! thank you, and yes I managed to solve it .


Tags 
arithmetic, elementary, functions, problems 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Questions Regarding Elementary Complex Functions  pirateprogrammer  Complex Analysis  3  September 11th, 2016 03:46 PM 
Elementary Differential Equation Problems  joseph95  Differential Equations  3  February 13th, 2014 12:56 PM 
Middle/Elementary Maths Problems  JamesTr  Elementary Math  2  January 3rd, 2014 09:06 PM 
A hypothesis on nonelementary functions  mathbalarka  Real Analysis  2  August 30th, 2012 04:37 AM 
2 elementary number theory problems....  earth  Number Theory  5  October 9th, 2010 05:54 AM 