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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: 1,428 Thanks: 352 
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: 3,330 Thanks: 219  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: 6,275 Thanks: 516  Quote:
 
February 5th, 2017, 02:28 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 17,709 Thanks: 1357 
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 

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