Euler's Equation Approach for Odd Perfect Numbers based on Wilson's Theorem Primality Condition
Abstract
This work proposes a modular technique inspired by Wilson's Theorem to investigate the Eulerequation for odd perfect numbers. A congruence in the form of the Wilson condition for primes was derived,imposing strong restrictions on the multiplicative orders of prime factors. From this, systematic exclusions wereestablished for the Eulerian prime and the primes of n². Finally, the combined requirements of order, generatordensity, and growth are presented, which force a structural conflict with the Euler form, eliminating candidatesfor odd perfect numbers.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Mathematical Theories
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 3 February 2026
- Language
- PT
- Document type
- Preprint