20200618, 11:56  #1 
"murat"
May 2020
turkey
61 Posts 
abouth perfect numbers 1
is it known property of perfect number or new ?
a is prime number which is diffferent from 3 . the number b = 3 x a² the plus signed integers of sum of divisors of b which is except from b is equal to ( a + 2 )² just like 3 x 5² = 75 1 + 3 + 5 + 15 + 25 = 49 
20200618, 12:13  #2 
"Oliver"
Sep 2017
Porta Westfalica, DE
2^{4}×23 Posts 
What does it have to do with perfect numbers?
Lets have \(p\) prime, not 3. Then the divisors of \(3p^2\) are \(1, 3, p, 3p, p^2, 3p^2\). You want to exclude the last one. Now we sum: \(1 + 3 + p + 3p + p^2 = 4 + 4p + p^2 = (p + 2)^2\). \(\blacksquare\)

20200618, 12:19  #3 
Jun 2003
7×683 Posts 
The sum is called aliquot sum

20200618, 12:27  #4  
"murat"
May 2020
turkey
3D_{16} Posts 
Quote:


20200618, 16:48  #5 
Nov 2003
2^{6}·113 Posts 

20200618, 17:16  #6 
Romulan Interpreter
Jun 2011
Thailand
10001011100100_{2} Posts 
Elementary my dear Watson... a perfect number is equal to sum of its proper divisors, so you solve the equation \(3p^2 = 4 + 4p + p^2 = (p + 2)^2\), and not only that you found an odd perfect number, which nobody was ever able to find, but moreover, you found something even rarer, an irrational odd perfect number!

20200618, 17:31  #7 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{3}×3×197 Posts 
Misc Math?

20200618, 17:41  #8 
"murat"
May 2020
turkey
3D_{16} Posts 

20200618, 17:55  #9  
"Oliver"
Sep 2017
Porta Westfalica, DE
2^{4}×23 Posts 
Quote:
Reading again, I think you were sarcastic, but I'm not good at this. Yes, I'd like the odd perfect number problem being solved. 

20200618, 18:16  #10 
Romulan Interpreter
Jun 2011
Thailand
2^{2}·7·11·29 Posts 
The sarcasm was not directed towards you. I was just saying (in my own way) that indeed, the story had nothing to do with perfect numbers. In fact, if the OP would have clicked the link from axn, (s)he would have found all the answers, and not needing any other "adocuate" (sic) site about pn's.
Last fiddled with by LaurV on 20200618 at 18:18 
20200618, 18:30  #11  
"murat"
May 2020
turkey
61 Posts 
Quote:


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