Mason's theorem with a difference radical

Katsuya Ishizaki; Risto Korhonen; Nan Li; Kazuya Tohge

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arXiv · 1806.00209

Mason's theorem with a difference radical

Katsuya Ishizaki·Risto Korhonen·Nan Li·Kazuya Tohge

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Abstract

Differential calculus is not a unique way to observe polynomial equations such as $a+b=c$. We propose a way of applying difference calculus to estimate multiplicities of the roots of the polynomials $a$, $b$ and $c$ satisfying the equation above. Then a difference $abc$ theorem for polynomials is proved using a new notion of a radical of a polynomial. Two results on the non-existence of polynomial solutions to difference Fermat type functional equations are given as applications. We also introduce a truncated second main theorem for differences, and use it to consider difference Fermat type equations with transcendental entire solutions.

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Katsuya Ishizaki, Risto Korhonen, Nan Li, Kazuya Tohge. 2018-06-01. Mason's theorem with a difference radical. https://arxiv.org/abs/1806.00209

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