
Math General Math Forum  For general math related discussion and news 
 LinkBack  Thread Tools  Display Modes 
February 2nd, 2017, 08:38 PM  #1 
Member Joined: Oct 2016 From: labenon Posts: 33 Thanks: 4  Perfect Numbers
I was searching some mathematical formulas and come across this question. Can any one help me to solve this.? I studied that a perfect number is one which equals the sum of its proper divisors. For example: the number 18 is abundant since 18 is less than 1 + 2 +3 + 6 + 9 =21, the number 15 is deficient since 15 is greater than 1+3+5 =9 and 6 =1+ 2 + 3 is perfect. Then I found the equation to find perfect even numbers : m = 2^(p1) * (2^p  1) , where p is prime number. Now the main question is from this equation : Can we find how many even & odd perfect numbers are there? 
February 2nd, 2017, 08:46 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,572 Thanks: 379 
It's an open question as to whether any odd perfect numbers exist. This is a famous problem in math. Here's an article about it. They've checked up to $10^{300}$ and not found any. That's $1$ with $300$ zeros. But compared to all the natural numbers that there are, it's just a drop in the bucket. Odd Perfect Numbers: Do They Exist? 
February 3rd, 2017, 03:53 AM  #3 
Newbie Joined: Dec 2016 From: United Kingdom Posts: 14 Thanks: 1 
I think this is still debatable questions, still I have found one article which can help you to solve this: Odd Perfect Number  from Wolfram MathWorld 
February 4th, 2017, 02:06 PM  #4  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Quote:
Did you see the credit given at the bottom of this wolfram link for contributing information? Our very own CRGreathouse!!! What a wonderful surprise and delight  
February 5th, 2017, 01:47 PM  #5  
Global Moderator Joined: May 2007 Posts: 6,343 Thanks: 534  Quote:
 
February 5th, 2017, 02:28 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 18,053 Thanks: 1395 
Yes. Note that 2^p  1 needs to be prime as well for m to be a perfect number. It's not known whether the number of perfect numbers is finite.

February 5th, 2017, 09:33 PM  #7 
Member Joined: Oct 2016 From: labenon Posts: 33 Thanks: 4  Perfect Numbers 

Tags 
numbers, perfect, prime 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
About odd perfect numbers  McPogor  Number Theory  10  April 10th, 2014 06:52 AM 
Perfect numbers  mathbalarka  Number Theory  4  September 1st, 2012 02:27 PM 
Perfect Numbers  Wissam  Number Theory  18  July 25th, 2010 12:34 AM 
About perfect even numbers  momo  Number Theory  14  April 27th, 2009 05:18 PM 
perfect numbers and amicable numbers  soandos  Number Theory  2  November 27th, 2007 04:42 AM 