A New Generalization of Fermat's Last Theorem

@article{Cai2013ANG,
  title={A New Generalization of Fermat's Last Theorem},
  author={T. Cai and D. Chen and Y. Zhang},
  journal={arXiv: Number Theory},
  year={2013}
}
  • T. Cai, D. Chen, Y. Zhang
  • 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{equation} \begin{cases} A+B=C ABC=D^n \end{cases} \end{equation} 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… CONTINUE READING
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