| 多项式（1＋x）^k＋（1-x）^k-2^k的整除性问题 |
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| 引用本文： | 杨婷,周佳馨,杨仕椿. 多项式（1＋x）^k＋（1-x）^k-2^k的整除性问题[J]. 成都大学学报(自然科学版), 2014, 33(4): 334-336 |
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| 作者姓名： | 杨婷 周佳馨 杨仕椿 |
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| 作者单位： | 阿坝师范高等专科学校数学与财经系,四川汶川,623000 |
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| 基金项目： | 四川省教育厅自然科学基金 |
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| 摘 要： | 对于整数k,设Tn（x）=（1＋x）^k＋（1-x）^k-2^k,设m,n为正整数,且m4,均有T4（x）不整除Tn（x）.
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| 关 键 词： | 多项式 整除 同余 递推序列 |
Divisibility Problem of Polynomial (1 + x)k + (1-x)k-2k |
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| YANG Ting,ZHOU Jiaxin,YANG Shichun. Divisibility Problem of Polynomial (1 + x)k + (1-x)k-2k[J]. Journal of Chengdu University (Natural Science), 2014, 33(4): 334-336 |
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| Authors: | YANG Ting ZHOU Jiaxin YANG Shichun |
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| Affiliation: | YANG Ting;ZHOU Jiaxin;YANG Shichun;Department of Mathematics and Finance,ABa Teachers College; |
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| Abstract: | For any positive integer k,let Tn（x） =（ 1 ＋ x）^k＋（ 1-x）^k-2^k. We set m,n to be positive integers,and let m n. The problem of divisible relationship Tm（ x） ｜ Tn（ x） was first proposed in 1980 by Tu. Bombieri and other scholars have gained some conclusions about this problem. Using the congruence relationship,the general term of the recursive sequence and the nature of the complex modulus,we prove that for any positive integer n 4,T4（ x） is not divisible by Tn（ x）. |
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| Keywords: | polynomial divisibility congruence recursive sequence |
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