恒整除  

Permanent Divisibility

作　　者：李秀萍[1] 刘明海 

机构地区：[1]山西财经学院基础部 [2]山西师大物理系

出　　处：《山西师大学报（自然科学版）》1994年第4期8-14,共7页Journal of Shanxi Teachers University(Natural Science Edition)

摘　　要：本文考察了正整数和整系数多项式之间的恒整除关系，给出了素数幂p^n(a≤p)恒整陈整系数多项式f(x)的简易判别法．从而对整系数多项式也得到了恒因子的求法．In this paper, we discussed the permanent divisibility relation between a power of prime and a polynomial with integral coefficients, obtained a simpler decision algorithm using the decision matrix, namely the following:Theorem. Assume f(x) =a0 + alx+…+anxn, (an≠0) p is a prime, a<p, then pa||f(x) if and only if p' |aa-i and Jp (f(a-i)(x)) is divisible for evern i = 1 ,2,…,a-1.

关 键 词：整除 整系数多项式 素数幂 判别法 正整数 因子 求法 简易 考察 

分 类 号：O156[理学—数学] G633[理学—基础数学]