# 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{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… Expand
3 Citations
The Proof of the Fermat’s Conjecture in the Correct Domain
The distinction between the Domain of Natural Numbers and the Domain of Line gets highlighted. This division provides the new perception to the Fermat’s Conjecture, where to place it and how to proveExpand
The y-Increment Puzzle, the Law-of-Large-Numbers, and a Second New Proof of Fermat’s Last Conjecture.
This article introduces a second new proof of Fermat’s Last Conjecture (Nwogugu  introduced the first new proof of Fermat’s Last Conjecture) which is studied in the context of Sub-Rings ofExpand
Why did Fermat believe he had ‘a truly marvellous demonstration’ of FLT?
Conventional wisdom dictates that proofs of mathematical propositions should be treated as necessary and sufficient for entailing significant mathematical truths only if the proofs are expressed inExpand