基于二项式定理应用的探究

二项式定理是初等数学中的一个重要定理，其形成过程是组合知识的应用，同时也是进一步学习概率统计的准备知识，在高等数学中更是许多重要公式的共同基础。从一个新的角度审视二项式定理，给出数环中一类数的n次幂计算的递推公式。同时利用二项式定理的推广形式——多项式定理，得到初等数论中费尔马小定理的一个新证明。

Explore and Study on AppliCation of Binomial Theorem

The binomial theorem is an important formula in elementary mathematics.Its formation process is the combination of knowledge and the preparation for study on probability statistics in future;it is the common basis of higher mathematics in many important formulas too.In this paper,we look at the binomial theorem from another perspective,and obtain the recurrence formula for calculation nth power of a class of numbers in ring.On the other hand,we give a new proof of Fermat's Little Theorem from the multinomial theorem that is the extension of binomial theorem.