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- W3091730427 abstract "Abstract Differential calculus is not a unique way to observe polynomial equations such as $$a+b=c$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>+</mml:mo> <mml:mi>b</mml:mi> <mml:mo>=</mml:mo> <mml:mi>c</mml:mi> </mml:mrow> </mml:math> . 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. Results, for example, on the non-existence of polynomial solutions to difference Fermat and difference Super-Fermat functional equations are given as applications. We also introduce a truncated second main theorem for differences, and use it to consider these functional equations with non-polynomial entire solutions. Equations with polynomial or non-polynomial solutions are observed to see the sharpness of results obtained." @default.
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- W3091730427 date "2020-09-28" @default.
- W3091730427 modified "2023-10-17" @default.
- W3091730427 title "A Stothers–Mason theorem with a difference radical" @default.
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- W3091730427 doi "https://doi.org/10.1007/s00209-020-02604-7" @default.
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