# A New Generalization of Fermat's Last Theorem

@article{Cai2013ANG,
title={A New Generalization of Fermat's Last Theorem},
author={Tianxin Cai and Deyi Chen and Yong Zhang},
journal={arXiv: Number Theory},
year={2013}
}
• Published 2013
• Mathematics
• arXiv: Number Theory
In this paper, we consider some hybrid Diophantine equations of addition and multiplication. We first improve a result on new Hilbert-Waring problem. Then we consider the equation $$\begin{cases} A+B=C ABC=D^n \end{cases}$$ where $A,B,C,D,n \in\ZZ_{+}$ and $n\geq3$, which may be regarded as a generalization of Fermat's equation $x^n+y^n=z^n$. When $\gcd(A,B,C)=1$, $(1)$ is equivalent to Fermat's equation, which means it has no positive integer solutions. We… Expand
3 Citations

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