整系数多项式的哥德巴赫命题

• 作 者: 仲木
• 出 处: 数学教学通讯
• 发表日期: 1981年02期
• 关键词: 整系数多项式 数学爱好者 施坦 不可约多项式 艾森 判定法 文中 《高等代数》 张禾 奇偶

我们熟知整数的哥德巴赫命题是:每一个大于2的偶数都可写成两个质数的和。这个命题的正确性至今尚未得到证明。在《数学爱好者》1980,1期刊载的《容易证明的“1+1”》(以下简称文[1])一文中提出了一个有兴趣的定理: 定理1.每一个整系数n(≥1)次多项式可写为两个n次不可约整系数多项式的和。这个定理的证明依赖于下述整系数多项式不可约的艾森施坦因判定法则定理2.整系数多项式 f(x)=a_0x~n+a_1x~(n-1)+…+a_(n-1)x+a_n (1)

The Goldbach proposition that we know about integers: Every even number greater than 2 can be written as the sum of two prime numbers. The correctness of this proposition has not yet been proved. In the article “Easily Proven “1+1”” (hereinafter abbreviated as [1]) contained in “Amateur of Mathematics” 1980,1, an interesting theorem is proposed: Theorem 1. Each integral coefficient n (≥ 1) The minor polynomial can be written as the sum of two n-time polynomials with irreducible integer coefficients. The proof of this theorem relies on the following Eisenstein’s law of irreducibility for polynomial integer coefficients. Theorem 2. Integer coefficient polynomial f(x)=a_0x~n+a_1x~(n-1)+...+a_(n- 1) x+a_n (1)