中文摘要：

利用Weil型特征标和数估计，证明Grannell—Griggs—Murphy定理对于一切满足q 7（mod12）的素数幂-q成立，改进了现有文献中所得到的定理对于不超过75079的12n＋7型素数p成立的结论．

英文摘要：

In this paper, Weil＇s estimate on character sums is employed to show that Grannell- Griggs-Murphy＇s theorem is true for every prime power q with q 7（mod 12）, which improves the existing result that this theorem is true for each prime p satisfying that p ≤ 75079 and p -- 7（rood 12）.