The Yorsh Theorem

A Formal Proof of the Non-Existence of Odd Perfect Numbers — Resolving a 2,300-year-old mathematical challenge

Interactive 3D Visualization

Explore the mathematical properties of divisors that prove the non-existence of odd perfect numbers through our interactive 3D visualization tool.

Resources & Downloads

Academic Paper

Access the complete formal proof, mathematical derivations, and rigorous analysis in this peer-reviewed academic document.

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Interactive Notebook

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About the Theorem

Theorem Statement

"No odd perfect number satisfies \( \sigma(N) = 2N \)"

The Yorsh Theorem provides a conclusive proof that odd perfect numbers cannot exist in the mathematical universe, resolving one of the oldest unsolved problems in number theory.

The proof employs structural contradiction from Euler's form, analyzing the behavior of the divisor sum function \( \sigma(N) \) for odd integers with the specific structure required of potential odd perfect numbers.

By demonstrating that \( \sigma(N) > 2N \) for any odd number with the requisite prime factorization, the theorem establishes the non-existence of odd perfect numbers by contradiction.

About the Author

Jorge Luis Álvarez Álvarez

Colombia

Cybrix Studios S.A.S.

yorshalvarez@cybrixstudios.com

Jorge Luis Álvarez Álvarez Founder and Creative Director of Cybrix Studios Jorge Luis Álvarez Álvarez is an innovator in the digital world, specializing in augmented reality, virtual reality, video game development, and 2D/3D animation. With a forward-thinking vision, he has led technological projects that transform the way people interact with digital content. As the founder and creative director of Cybrix Studios, based in Medellín and New Jersey, he leads a multidisciplinary team that merges creativity and technology to develop immersive digital experiences across sectors such as marketing, education, and entertainment.

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