Corpus ID: 14818194

Divisibility by 3 of even multiperfect numbers of abundancy 3 and 4

@inproceedings{Broughan2010DivisibilityB3,
  title={Divisibility by 3 of even multiperfect numbers of abundancy 3 and 4},
  author={K. Broughan and Q. Zhou},
  year={2010}
}
We say a number is flat if it can be written as a non-trivial power of 2 times an odd squarefree number. The power is the “exponent” and the number of odd primes the “length”. Let N be flat and 4-perfect with exponent a and length m. If a 6≡ 1 mod 12, then a is even. If a is even and 3 ∤ N then m is also even. If a ≡ 1 mod 12 then 3 | N and m is even. If N is flat and 3-perfect and 3 ∤ N, then if a 6≡ 1 mod 12, a is even. If a ≡ 1 mod 12 then m is odd. If N is flat and 3 or 4-perfect then it is… Expand
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A perfect number is a number whose divisors add up to twice the number itself. The existence of odd perfect numbers is a millennia-old unsolved problem. This note proposes a proof of the nonexistenceExpand

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Mathematics Subject Classification: Primary 11A05; Secondary 11A51. Keywords: multiperfect number, flat number, abundancy
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