生活资料只能按算术级数增长。

Subsistence only increases in an arithmetic ratio .

证明不存在四个连续的二项系数成算术级数。

Prove that no four consecutive binomial coefficients can be in arithmetic progression.

知识资源的使用价值呈几何级数增长 ，而知识资源的交换价值则呈现出算术级数与几何级数交互增长。

The exchangeable value of knowledge resources has non equal valuableness, duality of non stability and stability, and expansibility.

算术级数：一个数量在其变化的过程中，每一次变化后的量是变化前的若干倍，也就是乘积的关系。

Arithmetic progression: a number of its change in the process, after each change in the amount of change several times before, that is the product of the relationship.

利用解析数论工具证明了算术级数数列中素数幂分布的若干结果，这些结果在提供RBIBD设计与PMD设计的渐近存在性定理的精确定界时具有重要作用。

We present several theorems on the distribution of prime powers. These results play a very important role in providing explicit bounds for the asymptotic existence theorems of RBIBD and PMD.