# Mason's theorem with a difference radical

@article{Ishizaki2018MasonsTW, title={Mason's theorem with a difference radical}, author={Katsuya Ishizaki and Risto Korhonen and Nan Li and Kazuya Tohge}, journal={arXiv: Complex Variables}, year={2018} }

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…

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