[代數] polynomial
一個簡單的是非題
Every irreducible polynomial in Z[x] is primitive
(A polynomial f(x)=a_nx^n+...+a_1x+a_0 is said to be primitive if the gcd
of all coeficients is 1)
答案是給false
但是我覺得
Given a poly. f(x)=a_nx^n+...+a_1x+a_0 is irreducible.
If f is not primitive then, gcd(a_n,...,a_0)=d>1
a_n a_1 a_0
then f=d*g(x) ,where g(x)=-----x^n+...+-----x+-----
d d d
Since the only units in Z[x] are ±1
hence, f is not irreducible. →←
可以問一下我的證明哪裡有錯誤或是觀念有錯嗎？
還是單純的只是答案錯了？
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