mersenneforum.org Odd Perfect Number is 36k+9 ?
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 2014-07-20, 07:07 #1 isaac   "Isaac" Jul 2014 Israel 1102 Posts Odd Perfect Number is 36k+9 ? can someone review my work Odd Perfect Number is 36k+9 viXra.org e-Print archive, viXra:1407.0143, Odd Perfect Number is 36k+9 PDF link: http://www.vixra.org/pdf/1407.0143v1.pdf i asked around on the internet a lot of people and no one is yet to reply if i have a mistake then people should have said by now where it is and if this proof is valid then i don't get it ... why don't they say its ok? can someone take a look please?
2014-07-21, 02:16   #2
wblipp

"William"
May 2003
New Haven

23·5·59 Posts

Quote:
 Originally Posted by isaac Odd Perfect Number is 36k+9
I haven't looked at your paper yet. Are you aware of Jacques Touchard's proof in 1953 that an odd perfect number is either 12k+1 or 36k+9? If not, then the lack of response you have received is probably the result of a perception of unprofessionalism.

 2014-07-21, 09:44 #3 Pascal Ochem     Apr 2006 5F16 Posts Your mistake is page 3 when you say 3 | (P^{alpha+1}/(2*(P-1))) Take P=13 and alpha=1. Then P^{alpha+1}/(2*(P-1)) = (13^2-1)/(2*(13-1)) = (13+1)/2 = 7. And 7 is not divisible by 3. This is because in the previous line r = 3*t/w, you missed the case where w is divisible by 3, so that the factor 3 is canceled.
2014-07-21, 13:30   #4
CRGreathouse

Aug 2006

5,939 Posts

Quote:
 Originally Posted by Pascal Ochem Your mistake is page 3 when you say 3 | (P^{alpha+1}/(2*(P-1)))
Oh good, this is just the mistake I found when he brought up the same proof on http://mymathforum.com/ .

2014-07-22, 20:43   #5
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by CRGreathouse Oh good, this is just the mistake I found when he brought up the same proof on http://mymathforum.com/ .
Congrats on you supermod privileges. on the side of odd perfect numbers where's the thread where we talked about them and what's changed from:
Quote:
 In 1896, Stuyvaert stated that an odd perfect number must be a sum of two squares (Dickson 2005, p. 28). In 1887, Sylvester conjectured and in 1925, Gradshtein proved that any odd perfect number must have at least six distinct prime factors (Ball and Coxeter 1987). Hagis (1980) showed that odd perfect numbers must have at least eight distinct prime factors, in which case, the number is divisible by 15 (Voight 2003).
I know it was significantly increased last time I asked, I just thought that since I realized a condition for when 2n+1 divides 2k+1 ( not to confuse these with any variables used in the mathworld page I quoted) that it might be able to thin out the values in 36k+9 that were possible in my head because we could say if 2n+1 divides 36k+9 then k fits into this modulo class for each individual n or come up to a value that we can use as a higher modulus and remainder value to help out with.

2014-07-22, 22:18   #6
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by science_man_88 Congrats on you supermod privileges. on the side of odd perfect numbers where's the thread where we talked about them and what's changed from: I know it was significantly increased last time I asked, I just thought that since I realized a condition for when 2n+1 divides 2k+1 ( not to confuse these with any variables used in the mathworld page I quoted) that it might be able to thin out the values in 36k+9 that were possible in my head because we could say if 2n+1 divides 36k+9 then k fits into this modulo class for each individual n or come up to a value that we can use as a higher modulus and remainder value to help out with.
I just realized that this only helps if we take the value of k in 36k+9 realize it equates to n=(k*18+4) expressed in 2n+1, as equal to another equation for all the $n_i$ for the $2n_i+1$ but this gives a modulus of 36k+9 and at best gives an equation that n fits based on the other n values.

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