• Corpus ID: 116974690

Solving the Odd Perfect Number Problem: Some Old and New Approaches

@article{Dris2012SolvingTO,
  title={Solving the Odd Perfect Number Problem: Some Old and New Approaches},
  author={Jose Arnaldo B. Dris},
  journal={arXiv: Number Theory},
  year={2012}
}
A perfect number is a positive integer $N$ such that the sum of all the positive divisors of $N$ equals $2N$, denoted by $\sigma(N) = 2N$. The question of the existence of odd perfect numbers (OPNs) is one of the longest unsolved problems of number theory. This thesis presents some of the old as well as new approaches to solving the OPN Problem. In particular, a conjecture predicting an injective and surjective mapping $X = \sigma(p^k)/p^k, Y = \sigma(m^2)/m^2$ between OPNs $N = {p^k}{m^2… 

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