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Topic: formal proof that No Odd Perfect Number exists #1339 Correcting Math
Replies: 11   Last Post: Jan 3, 2014 7:17 PM

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 plutonium.archimedes@gmail.com Posts: 8,733 Registered: 3/31/08
formal proof that No Odd Perfect Number exists #1339 Correcting Math
Posted: Dec 31, 2013 6:10 AM

formal proof that No Odd Perfect Number exists #1339 Correcting Math

Alright, it is really late for me and I should have been in bed hours ago, but this has kept me up and taking a hot shower, I am ready to write up the proof formally.

I am tired at this moment so will write it in depth tomorrow.

The main features are selected from my previous posts of this proof. Basically the proof relies on the numerator of an odd number with its cofactors is even, and to be odd perfect requires 2k/k = 2 where k is the odd number. The contradiction comes when we realize the k in the numerator as a addition of the cofactors is even.

So we have as cofactors (f1/k + f2/k) + (f3/k + f4/k) + . . + (fn/k + fm/k) = 2 for an odd perfect number.

The summation of the numerator ends up being even, so we have even/k = 2, and since we supposed k to be odd perfect we have 2even/k = 2.

Now the only time that k divides into the numerator and yields 2 is when k is odd perfect, and all other times of the division of k into 2even is a fraction.

Now we manipulate the equation and we have 2*2 small-odd/k. We know the numerator is even and so we reduce it by retreiving the 2 and we suppose it is reduced to lowest terms (that is the numerator is not further divisible by 2).

So we have at this stage, we have 2*2(smaller odd)/k = 2. Here we note that smaller odd just means it is a odd number smaller than is k.

Now we arrive at a contradiction for we divide both sides by 2 and we have as the odd perfect number, we have 2(smaller odd) = odd and thus we have 2odd = odd, a contradiction.

I will condense the above tomorrow. I think the final formal proof is about 2 paragraphs long. But the talk and exploration leading up to this proof is what allows me to condense it into a formal proof.

P.S. can someone at Google please stop these moderators from holding-up and delaying my posts from appearing on the newsboard for hours or days from whence I sent the post. It is difficult to maintain coherence when posts are scattered hours apart.
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Recently I re-opened the old newsgroup of 1990s and there one can read my recent posts without the hassle of mockers and hatemongers.