摘要
对高斯函数的两个恒等式：，其中其中ｐ、ｑ是正奇数且（Ｐ，ｑ）＝１，以及Ｔｏｍ．Ｍ．Ａｐｏｓｔｏｌ的一个问题“若α＝１，２，３，４，５，６，７．证明存在一个（依赖于α的）整数ｂ，使得，作了进一步的推广，得到一般性的结论．
The paper made a further extension and a general conclusion of two identities of Gauss function: andp,q as positive odd numbers and (p,q) =1. Aquestion of Tom. M. Apostol, if a =1, 2, 3, 4, 5, 6, 7, an integer b depending on a exsits,thus was spread and concluded.
