论文标题
p-th循环多项式的不可约性的替代证明
An alternative proof for the irreducibility of the p-th cyclotomic polynomial
论文作者
论文摘要
令$ p $为主要数字。作为艾森斯坦不可约性标准的标准应用，众所周知，$ p $ - th环环多项式$φ_p（t）= 1+t+t+dots+t+t+t {p-1} $是$ e^{2πi/p} $ bacy $ e^$ $ \ nathbb =} $ e^{2πi/p} $的最小多项式。该注释提供了替代性证明，利用决定因素证明由于Kronecker而证明了引理。
Let $p$ be a prime number. As a standard application of the irreducibility criterion of Eisenstein, it is well known that the $p$-th cyclotomic polynomial $Φ_p(t)=1+t+\dots+t^{p-1}$ is the minimal polynomial of $e^{2πi/p}$ over $\mathbb{Q}$. This note provides an alternative proof, utilizing determinants to prove a lemma due to Kronecker.
