论文标题
关于Golomb猜想的概括
On the generalization of Golomb's conjecture
论文作者
论文摘要
让$ p $成为足够大的质量，$ r $是任何给定的正整数。假设$ a_1，\，\ dots，\，a_r $是成对的，而不是零modulo $ p $。令$ n（a_1，\，\ dots，\，a _r; \，p）$表示$α_1，\，\，\ dots，\，α_r，\，β$的$ primots modulo $ $ p $的$α_1，\，\ dots的数量，例如$α_1_1+α_1+β\ equiv a_1，\ equiv a_1，\ e y \ \ \ \ \ \ \ \ \ \ \ \ \，\， a_r \，（{\ rm mod} \，p）。$在本文的第一个版本中，我们证明了$ n的渐近公式（a_1，\，\ dots，\ dots，\，a_r; \，p）$，以便我们可以回答wenpeng zhang and tingting wang wang wang wang。但是我们发现我们的结果已包括在1956年的L. Carlitz论文中，这在下面的其他评论中进行了解释。
Let $p$ be a sufficiently large prime number, $r$ be any given positive integer. Suppose that $a_1,\,\dots,\,a_r$ are pairwise distinct and not zero modulo $p$. Let $N(a_1,\,\dots,\,a_r;\,p)$ denote the number of $α_1,\,\dots,\,α_r,\,β$, which are primitive roots modulo $p$, such that $α_1+β\equiv a_1,\,\dots,\,α_r+β\equiv a_r\,({\rm mod}\,p).$ In the first version of this paper, we proved an asymptotic formula for $N(a_1,\,\dots,\,a_r;\,p)$ so that we could answer an open problem of Wenpeng Zhang and Tingting Wang. But we found that our result had been included in a paper of L. Carlitz in 1956, which is explained in the additional remark below.
