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
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Authors and affiliations

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


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.


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

AMS Classification

  • 11D57
  • 11T55
  • 65H04


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

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