Do Quasiperfect Numbers Really Exist?

  • Thread starter Thread starter Joseph Fermat
  • Start date Start date
  • Tags Tags
    Numbers Proof
Click For Summary
Quasiperfect numbers are defined as numbers for which the sum of their divisors equals one minus twice the number, represented mathematically as σ(n) = 2n + 1. The existence of such numbers remains an open question in mathematics. A user claims to have developed a proof demonstrating that quasiperfect numbers do not exist by creating an impossible situation for their existence. However, another participant points out a flaw in the proof's logic, indicating that a critical equation transition is incorrect. The original poster acknowledges the mistake and seeks further assistance to refine their argument.
Joseph Fermat
Messages
7
Reaction score
0
A Quasiperfect number is any number for which the sum of it's divisors is equal to one minus twice the number, or a number where the following form is true,

σ(n)=2n+1​


One of the well known and most difficult questions in mathematics is whether such numbers exist at all. I have created a rather interesting proof to show that quasiperfect numbers do not exist. I use a process of transformation to create a situation necessary for the existence of a quasiperfect number, and then show that such a situation is impossible, therefore disproving the possibility of a quasiperfect number.

View attachment On the Nonexistence of Quasiperfect Numbers.pdf
 
Last edited:
Physics news on Phys.org
Why not use the same argument with n=2x+1 to prove that odd numbers do not exist?
 
Hi, Joseph,
there is a problem when going from eq.8 to eq.9: 1 - (h(n) - 2) is not -(h(n)+1) (which is negative), but 3 - h(n) (which is positive).
 
Dodo said:
Hi, Joseph,
there is a problem when going from eq.8 to eq.9: 1 - (h(n) - 2) is not -(h(n)+1) (which is negative), but 3 - h(n) (which is positive).
Which would mean that my proof is fallous.:redface: Oh, well back to the drawing board. Anyone have any ideas where to go from here. Any help would be appreciated.
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
View full post »

Similar threads

Graduate A thought on the existence of an odd perfect number
  • · Replies 6 ·
Replies
6
Views
1K
Undergrad Fundamental theorem of arithmetic from Jordan-Hölder theorem
  • · Replies 5 ·
Replies
5
Views
2K
High School Two interesting number theory tricks
  • · Replies 3 ·
Replies
3
Views
727
The proof that an odd perfect number does not exist
  • · Replies 6 ·
Replies
6
Views
11K
Undergrad Questions regarding Kurepa's Conjecture
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Does there exist a proof for these conjectures?
  • · Replies 2 ·
Replies
2
Views
2K
High School Does the L2 norm of a vector destroy all directional info?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad I think I've hit upon a very easy proof of impossibility of quintic
  • · Replies 2 ·
Replies
2
Views
2K
Number Theory proof linked to decimals
  • · Replies 5 ·
Replies
5
Views
4K
High School How can hyperreal numbers make infinitesimals logically sound in calculus?
  • · Replies 24 ·
Replies
24
Views
6K