费马方程在某些准素分量下无解
Fermat's Equation Has No Solution with Some Prime Components
摘要：
在初等数论的范围内，作为主要结果，我们证明了：如果$1 \leq x < y < z$是整数，使得至少有一个$y, z, x+y$是素数，则对每一个奇数$n \geq 3$都有$x^{n}+y^{n} \neq z^{n}$.这个结果覆盖了Abel猜想的一个特例，并给出了在$n$中构造无穷多个不一致满足Fermat方程的集态互质整数的一种确定方法.
英文摘要：
Within the scope of elementary number theory, we prove that, as the main result, if $1 \leq x < y < z$ are integers such that at least one of $y, z, x+y$ is prime then $x^{n}+y^{n} \neq z^{n}$ for every odd integer $n \geq 3$. This result covers a special case of a conjecture of Abel, and furnishes a definite way to construct infinitely many setwise coprime integers that do not satisfy the Fermat's equation uniformly in $n$.
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