生活资料只能按算术级数增长。
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.
什么是算术级数？
已有结论表明：素数集中存在任意长的算术级数。
It has been proved that the primes contain arbitrarily long arithmetic progressions.
解决了三素数定理推广到素数取自算术级数的问题。
Every large odd integer can be represeted as the sum of three primes which take from arithmetic progressions.
本文运用解析的方法，研究模为算术级数中素数的正规化三次高斯和在单位圆周上的分布。
In this paper, normalized cubic Gauss sums' distribution at unit circle is studied by analytical methods.
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.
本文给出了华罗庚五素数平方定理的算术级数形式，证明了其中一个素数可以取在大模的算术级数中。
In this paper, we generalize Hua's five primes squares theorem, and prove that one of the primes can be taken in arithmetic progressions with large moduli.
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.
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.
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.
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