论文标题
$ x^r + y^r = dz^p $的两个结果
Two results on $x^r + y^r = dz^p$
论文作者
论文摘要
本说明证明了两个有关fermat-type方程的定理$ x^r + y^r = dz^p $其中$ r \ geq 5 $是素数。我们的主要结果表明，对于无限的整数〜$ d $，以前的方程式没有非平凡的原始解决方案，因此对于一组指数的指数$ p $，$ 2 \中间x+y $或$ r \ r \ mid x+y $。我们将模块化方法带有一个符号参数来证明这一结果。
This note proves two theorems regarding Fermat-type equation $x^r + y^r = dz^p$ where $r \geq 5$ is a prime. Our main result shows that, for infinitely many integers~$d$, the previous equation has no non-trivial primitive solutions such that $2 \mid x+y$ or $r \mid x+y$, for a set of exponents $p$ of positive density. We use the modular method with a symplectic argument to prove this result.
