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.
On the Nonexistence of Quasiperfect Numbers.pdf