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
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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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Cite this paper
Davis, S. (2017). A conjecture on degrees of algebraic equations. Notes on Number Theory and Discrete Mathematics, 23(2), 84—90.