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Topic: Proof of No Odd Perfect Number beyond 1 exists #1441 Correcting Math
Replies: 1   Last Post: Jan 18, 2014 2:31 PM

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Brian Q. Hutchings

Posts: 6,427
Registered: 12/6/04
Re: Proof of No Odd Perfect Number beyond 1 exists #1441 Correcting Math
Posted: Jan 18, 2014 2:31 PM
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of course, "they did have such a definition, although
I also forget

> I bring up this issue because in Old Math, they never had a standard definition of what it means to be a divisor of a perfect number. Some left out the number itself so that for 6 they had the divisors as only 1,2,3 when it should include the 6. For 9 they had the divisors as 1,3 but in cofactors we know the divisors of 9 must be 1,3,3,9. Now why do we know that? Because mathematics has a strict definition of division and multiplication where both operations have three entities-- divisor, dividend and quotient and multiplier, multiplicand and product. So that the only sensible and uniform and logical way of confronting the No Odd Perfect Number is to define its divisors as cofactors, for otherwise, we lop off numbers that should not be lopped off out of sentiment or acting arbitrarily. It is this reason that Euclid could not prove No Odd Perfect, yet could prove square root of 2 is not rational, because he had no uniform and logical definition for divisor.

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