论文标题
整数上的一类多项式类别
An irreducible class of polynomials over integers
论文作者
论文摘要
在本文中，我们考虑$ f（x）= a_0+a_ {n_1} x^{n_1}+a_ {n_2} x^{n_2}+dots+a_r+a_r} x^n_r} x^^^^n_r} { | a_ {n_1} |+\ dots+| a_ {n_r} |，$ $ | a_0 | $是Prime Power，$ | A_0 | \ nmid | a_ {n_1} a_ {n_1} a_ {n_r} | $。我们将表明，在严格的不平等情况下，这些多项式对于某些$ n_1 $的值不可简化。在平等的情况下，除了其循环因素外，它们恰好具有一个不可还原的非重生因子。
In this article, we consider polynomials of the form $f(x)=a_0+a_{n_1}x^{n_1}+a_{n_2}x^{n_2}+\dots+a_{n_r}x^{n_r}\in \mathbb{Z}[x],$ where $|a_0|\ge |a_{n_1}|+\dots+|a_{n_r}|,$ $|a_0|$ is a prime power and $|a_0|\nmid |a_{n_1}a_{n_r}|$. We will show that under the strict inequality these polynomials are irreducible for certain values of $n_1$. In the case of equality, apart from its cyclotomic factors, they have exactly one irreducible non-reciprocal factor.
