odd-perfect numbers don't exist

[Bill Bouris]

Hello, Readers.

I have proven that odd-perfect numbers don't exist; it's a 1-page proof that combines Euler's work with that of Jacques Touchard's 1953-paper.

Anyone with the knowledge of basic algebra can enjoy it. The answer has been right under our noses!; please visit the root page of my website... www.oddperfectnumbers.com to see for yourself; no additional math is needed to construct this very valid proof. I've also included proofs of both Zarankiewicz's and Richard K. Guy's crossing number formulas on the page Other Short Proofs; just click on the heading to view them.

Best Regards,

Bill Bouris

[Uncwilly]

This is was posted in the wrong part of the forum.

That makes me think that the proof may have problems too.

[science_man_88]

Originally Posted by Uncwilly

This is was posted in the wrong part of the forum.

That makes me think that the proof may have problems too.

and a link to this site has been posted in another thread I swear ( think it got moved to the useless post thread or is in odd perfect number roadblocks

[CRGreathouse]

Paragraph 5 seems to contain the first mistake: "the first factor of the sum is always equal to one-third the size of the number being compared". The previous paragraphs have no mathematical content relating to odd perfect numbers.

[akruppa]

I have only skimmed the web page. Would you say this is Misc. Math. material?

[science_man_88]

Originally Posted by akruppa

I have only skimmed the web page. Would you say this is Misc. Math. material?

well it's definitely math related more than science or technology as to the judgement of misc. or not well most other things that aren't proven and claimed go to misc at last check.

[science_man_88]

Originally Posted by CRGreathouse

Paragraph 5 seems to contain the first mistake: "the first factor of the sum is always equal to one-third the size of the number being compared". The previous paragraphs have no mathematical content relating to odd perfect numbers.

if the op hasn't realized why maybe I could help:

okay Q=3 allows it

Q=6n+1 or 6n-1 means Q^2 is of the form 6n+1

to make it divisible by three (4x+1)^(4y+1) must be 0 mod 3:

1,5,9 = 1,2,0 mod 3 so the base doesn't always allow 0 mod 3 so next to the exponents so to ensure the biggest factor is 1/3 of the values of the number 1^(4x+1) ,2^(4y+1) , and 0^(4y+1) , must all be 0 mod 3 , and they aren't. even replacing Q=2 doesn't fix that 1^(4y+1) will always be one and hence with Q=2 it will end up as four ( and yes I know that 4 is already not included).

of course I'm not familiar to all requirement of the equation you talk of.

[CRGreathouse]

Originally Posted by akruppa

I have only skimmed the web page. Would you say this is Misc. Math. material?

Oh yes, no doubt.

[science_man_88]

Originally Posted by science_man_88

if the op hasn't realized why maybe I could help:

okay Q=3 allows it

Q=6n+1 or 6n-1 means Q^2 is of the form 6n+1

to make it divisible by three (4x+1)^(4y+1) must be 0 mod 3:

1,5,9 = 1,2,0 mod 3 so the base doesn't always allow 0 mod 3 so next to the exponents so to ensure the biggest factor is 1/3 of the values of the number 1^(4x+1) ,2^(4y+1) , and 0^(4y+1) , must all be 0 mod 3 , and they aren't. even replacing Q=2 doesn't fix that 1^(4y+1) will always be one and hence with Q=2 it will end up as four ( and yes I know that 4 is already not included).

of course I'm not familiar to all requirement of the equation you talk of.

in fact using PARI I've proven the first exception to 0 mod 3 to be 3125. if I coded it correct.

[akruppa]

Moved to Misc. Math.

[CRGreathouse]

Science man, I'm not sure what you're trying to show. Since you're talking about an odd perfect number Q must be odd, and hence Q ≠ 2. It's know that Q is divisible by at least eight different primes so in particular Q ≠ 3. 4x+1 is prime, so (4x+1)^(4y+1) is not 0 mod 3.