整系数多项式(x-a1)(x-a2)…(x-an)±p的不可约性研究OA
On the Irreducibility of Integral Coefficient Polynomial(x-a1)(x-a2)…(x-an)±p
本文研究了整系数多项式(x-a1)(x-a2)…(x-an)±p在有理数域上的不可约性.通过分析在整点上的取值性质,得到了当n为奇数且n≥9 时,对所有的素数p,该多项式在有理数域上均不可约;当n为偶数且n≥10时,若素数p<(n/2)!-1,则该多项式在有理数域上不可约.
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.
赵飞燕
南京师范大学数学科学学院,江苏 南京 210023
数理科学
整系数多项式有理数域不可约抽屉原理
integral coefficient polynomialrational number fieldirreduciblePigeon Hole Principle
《南京师大学报（自然科学版）》 2026 (1)
1-4,4
南京师范大学高等代数融合型课程项目.
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