中文摘要：

研究了一类Hash函数的Hash冲突问题。利用数论中关于整除的相关定理，完整地给出了一类Hash函数已经解决了Hash冲突的理论证明，为该函数的应用提供了可靠的理论基础。算例演示结果表明了该类Hash函数在寻找频繁项目集时的方便性和有效性。

英文摘要：

The Hash colliding problem for a kind of Hash functions is studied. By further researching the properties ofthese functions, theorems related to integer division is employed to prove that these functions can completely avoid Hash colliding, which provides reliable theoretical basis for their applications. An example is given to demonstrate that these functions are convenient and valid in finding frequent item-sets.