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Topic: New Method in proof that No Perfect Cuboid is constructible #1499
Correcting Math

Replies: 30   Last Post: Feb 11, 2014 2:20 PM

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 gnasher729 Posts: 419 Registered: 10/7/06
Re: New Method in proof that No Perfect Cuboid is constructible #1499
Correcting Math

Posted: Feb 9, 2014 9:04 PM

On Wednesday, February 5, 2014 12:40:13 AM UTC, Wizard-Of-Oz wrote:

> I don't see that that will lead to anything terribly useful unless one
> can prove that the list is inifinite which means there is no odd perfect
> number. But I can't see that there is a way to prove that it is
> inifinite or not OTHER THAN be proving there is no odd perfect number.
> So I can't see that it would help us arrive at such a prove, rather it
> would be a consquent of it being proven.

It's an interesting question on its own. How often do we get numbers that are how close to being perfect? Are there any odd numbers x other than x = 1, 3, 5 and 9 where the difference between the sum of divisors of x and 2x is less than 6? There are a few where the difference is exactly 6. Are there values k where the difference between the sum of divisors of x and 2x is less than k infinitely many times? If yes, which k?