20141116, 11:31  #1 
Nov 2014
1 Posts 
I think I found proof that no odd perfect numbers exist!
First, we can all agree that all perfect numbers are in the form (2^(n1))(2^n1), right?
So, if a number is odd, then it has two factors that are both odd. I can prove this by drawing a multiplication table. I'm just going to do 2 & 3, but you can check for yourself. 2 3 2 4 6 3 6 9 The only pair of factors that have an odd product are the factors that are both odd; 3 and 3. If this is the case, then if (2^(n1))(2^n1) equals a perfect number, then both 2^(n1) and (2^n)1 are odd. For (2^n)1, any number n will be odd, except for n=0, but (2^(01))(2^01) equals (1/2)(1), or 1/2, which is not an odd number, or a perfect number. For 2^(n1), only n=1 makes it odd, because 2^(11) = 1, but that would mean that the other factor would = (2^1)1 = 1. 1*1 = 1. Does this mean that 1 is an odd perfect number? Otherwise, there is no odd perfect number. 
20141116, 14:04  #2 
Jun 2014
120_{10} Posts 
It is only even perfect numbers that have that form. As well as this, one of the factors is even, because it is a power of 2.

20141116, 14:04  #3  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
3^{5}×5^{2} Posts 
Quote:
Quote:
Now there is just the small problem remaining to prove that an odd number can't be a perfect number. BTW: Even the Wikipedia page could have saved you all this embarrassment. 

20141116, 14:58  #4  
Nov 2003
1110100100100_{2} Posts 
Quote:


Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
perfect number proof  toilet  Homework Help  12  20121017 13:42 
oddperfect numbers don't exist  Bill Bouris  Miscellaneous Math  15  20110508 15:22 
Proof of Perfect Numbers  Vijay  Miscellaneous Math  10  20050528 18:11 
Perfect Numbers  MajUSAFRet  Math  3  20031213 03:55 
Odd Perfect Numbers  ZetaFlux  Math  1  20030528 19:41 