南京师大学报（自然科学版）2026，Vol.49Issue(1)：1-4,4.DOI:10.3969/j.issn.1001-4616.2026.01.001
整系数多项式(x-a1)(x-a2)…(x-an)±p的不可约性研究
On the Irreducibility of Integral Coefficient Polynomial(x-a1)(x-a2)…(x-an)±p
摘要
Abstract
This paper investigates the irreducibility of the integral coefficient polynomial(x-a1)(x-a2)…(x-an)±p over the rational number field.We have the conclusion that when n is odd and n≥9,for all prime numbers p,the polynomial is irreducible in the rational number field;when n is even and n≥10,if the prime number p<(n/2)!-1,then the polynomial is irreducible.关键词
整系数多项式/有理数域/不可约/抽屉原理Key words
integral coefficient polynomial/rational number field/irreducible/Pigeon Hole Principle分类
数理科学引用本文复制引用
赵飞燕..整系数多项式(x-a1)(x-a2)…(x-an)±p的不可约性研究[J].南京师大学报（自然科学版）,2026,49(1):1-4,4.基金项目
南京师范大学高等代数融合型课程项目. （）
