论文标题
在有限字段$ \ mathbb {z} _p $中的diophantine方程的解决方案$ x^n + y^n = z^n $
On the Solutions of the Diophantine Equation $x^n + y^n = z^n$ In the Finite Fields $\mathbb{Z}_p$
论文作者
论文摘要
令$ p $为Prime整数，$ \ Mathbb {Z} _p $订单$ P $和$ \ Mathbb {z}^{*} _ {p} $的有限字段是其多重环形组。我们认为diophantine方程$ x^n + y^n = z^n $，$ 1 \ leq n \ leq \ frac {p -1} {2} $。本文我们的主要目的是提供指数$ n $和prime $ p $之间的最佳条件或关系，以确定二磷剂方程的存在$ x^n + y^n = z^n $与$ 1 \ leq n \ leq n \ leq leq p -1 $，在有限firite fielite fields $ \ \ mathbb z z} _ p $中。
Let $p$ be a prime integer, $\mathbb{Z}_p$ the finite field of order $p$ and $\mathbb{Z}^{*}_{p}$ is its multiplicative cyclic group. We consider the Diophantine equation $x^n + y^n = z^n$ with $1 \leq n \leq \frac{p - 1}{2}$. Our main aim in this paper is to give optimal conditions or relationships between the exponent $n$ and the prime $p$ to determine the existence of nontrivial solutions of the diophantine equation $x^n + y^n = z^n$ with $1 \leq n \leq p -1 $, in finite fields $\mathbb{Z}_p$.
