
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 5th, 2017, 02:39 PM  #1 
Newbie Joined: May 2017 From: England Posts: 2 Thanks: 0  Using Totient to examine n = 4622
For the number of pairs (a,b) with a+b= 4622 and neither a nor b divisible by 2,3,5,7,11. I was told be a friend that the number of such pairs is found using Euler's Totient resulting in (32)*(52)*(72)*(112) Is this the case and can anyone explain how Euler's Totient is used to determine this? Be gentle with me..... 
May 5th, 2017, 06:01 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,817 Thanks: 760 
Did you google "Euler's Totient" ?

May 5th, 2017, 09:26 PM  #3 
Newbie Joined: May 2017 From: England Posts: 2 Thanks: 0 
Yes......I can see that the Totient applies to the first n integers but how does this help when I am examining a set of pairs of integers ? So for 2310 integers....the totient would be (21)*(31)*(51)*(71)*(111) = 480 However,again....how can I apply this to 2311 pairs? Last edited by Elaine; May 5th, 2017 at 09:41 PM. 
May 7th, 2017, 07:19 AM  #4 
Member Joined: Jan 2016 From: Athens, OH Posts: 82 Thanks: 40 
Elaine, Unless your friend's name is Socrates, I should have thought your friend would have explained the answer to you. Here's an explanation that I hope you can follow. If you're into computer programming, here's a little Java program that verifies the above proposition: Code: public static void main(String[] args) { int[] primes = {2, 3, 5, 7, 11}; int total = 0; int i, j, n = 2310; for (i = 1; i < n; i++) { for (j = 0; j < 5; j++) { if (i % primes[j] == 0) { break; } } if (j == 5) { for (j = 0; j < 5; j++) { if ((2 * n + 2  i) % primes[j] == 0) { break; } } if (j == 5) { total++; } } } System.out.println(total); } Last edited by johng40; May 7th, 2017 at 07:26 AM. 

Tags 
4622, examine, number theory, totient 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Examine the special relationship between the single and triple angles of an arbitrary  Deshichiu  Geometry  2  April 13th, 2017 04:30 AM 
Examine the special relationship between the single and triple angles of an arbitrary  Deshichiu  Geometry  2  March 13th, 2017 02:56 AM 
Examine the convergence of a sequence $\{a_{n}\}$ which is given by $a_{1}=a>0,a_{2}=  anonymous  Calculus  2  June 7th, 2015 09:14 PM 
Euler totient : phi(n)=phi(a)+phi(na)  Bogauss  Number Theory  8  March 22nd, 2012 09:04 AM 
A result concerning the totient  icemanfan  Number Theory  1  March 18th, 2012 12:41 PM 