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證明t^8-t^4+1 irreducilbe over Q 如果沒辦法的話,有沒有別的方法證明exp(i*pi/12)的minimal polynomial是t^8-t^4+1? -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 108.65.2.220
Sfly :cyclotomic polynomials are irr 04/24 09:24
calvin4 :let x = t^4. then the polynomial becomes x^2 - x 04/24 12:13
calvin4 :+ 1, which is irreducible over Q. the rest of the 04/24 12:14
calvin4 :proof is left to you. 04/24 12:15
wickeday :好奇樓上的方法要怎麼做,t^4-1是reducible但x-1是 04/24 14:55
wickeday :irreducible說。 04/24 14:56
calvin4 :我好像搞錯題型了。你說得對…… 04/25 02:27