A conjecture on degrees of algebraic equations

Simon Davis
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 2, Pages 84–90
Full paper (PDF, 175 Kb)

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Authors and affiliations

Simon Davis
Research Foundation of Southern California
8837 Villa La Jolla Drive #13595
La Jolla, CA 92039

Abstract

It is proven that the validity of a conjecture on the degrees of an algebraic equation consisting of three polynomials is determined by the derivatives. The result is extended to positive polynomials satisfying a generalized Fermat equation, after setting the exponents X, Y and Z equal to 1, and specialization to prime factors of the product of integer values of the polynomials yields the inequality equivalent to the abc conjecture.

Keywords

• Degrees
• Derivative
• Positive polynomials
• Square-free factor inequality

AMS Classification

• 11D57
• 11T55
• 65H04

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