Odd Perfect Number: A Proof at the Boundary of Number Theory baixar o livro de graça

What happens when the definition of a perfect number crosses zero?

Odd Perfect Number begins with Jeff Pittman’s independently developed handwritten argument that −1 is an odd perfect number. The book then asks the question mathematical rigor requires: what exactly does “perfect” mean once negative integers are admitted?

Pittman presents the original proof near the beginning, distinguishes it from the classical positive-integer definition, and develops an explicit signed extension called absolute-perfection. Within that extension, the book proves a clean classification theorem: −1 is the unique negative absolute-perfect integer, while the positive solutions remain the classical perfect numbers.

Written for curious readers without requiring advanced number theory, this concise essay explores divisors, absolute value, parity, mathematical definitions, objections, alternative extensions, and the difference between proposing a neighboring problem and solving the classical odd-perfect-number problem. It includes the original handwritten proof, a reader’s proof workshop, and complete solutions.

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