Why an odd perfect number, if exists, is not divisble by 3?

  • Thread starter Thread starter l-1j-cho
  • Start date Start date
Click For Summary
Mathematicians have established that an odd perfect number is not divisible by 3, 5, or 7. Despite efforts, a definitive proof for the non-divisibility by 3 remains elusive. It is noted that an odd perfect number must have at least 7 prime factors, a result attributed to Carl Pomerance, which is now believed to have a lower bound of 9 distinct prime factors. The discussion highlights the ongoing challenges in proving properties of odd perfect numbers. The quest for a proof continues to intrigue mathematicians.
l-1j-cho
Messages
104
Reaction score
0
So a number of mathematicans showed that an odd perfect number is not divisble by either 3, 5,or 7. I tried really hard to find a proof for that, but I haven't succeeded to do so.
Could anyone please help me to find a proof that an odd perfect nmber is not divisble by 3?
 
Physics news on Phys.org
never mind. it might
be divisible by 3, 5, or 7
 
the result i recall is that an odd perfect number has at least 7 prime factors. that result is some 40 years old, and due i believe to carl pomerance.
 
according to wiki the lower bound is now up to 9 distinct prime factors.
 

Thread 'Confusion about the Moyal-Weyl twist'

I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...
View full post »

Similar threads

Undergrad Questions about non existence of GCDs vs (coimages, cokernels)
  • · Replies 12 ·
Replies
12
Views
621
Graduate A thought on the existence of an odd perfect number
  • · Replies 6 ·
Replies
6
Views
1K
Perfect numbers beside 6 in mod6.
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad What is the probability that the product of the digits is odd?
  • · Replies 13 ·
Replies
13
Views
2K
The proof that an odd perfect number does not exist
  • · Replies 6 ·
Replies
6
Views
11K
MHB A Subset of a Graph with No Perfect Matching
  • · Replies 1 ·
Replies
1
Views
2K
Difference in Powers of Odd Primes
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Is this Recursive Pattern in the Collatz Sequence Known?
  • · Replies 3 ·
Replies
3
Views
789
A question about Stewart's calculus -- Contains answers to odd numbered questions?
  • · Replies 8 ·
Replies
8
Views
3K
Conjecture regarding perfect numbers.
  • · Replies 10 ·
Replies
10
Views
5K