jostpuur
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- 19
This claim is supposed to be true. Assume that p\in\mathbb{F}[X] is an irreducible polynomial over a field \mathbb{F}\subset\mathbb{C}. Also assume that
<br /> p(X)=(X-z_1)\cdots (X-z_N)<br />
holds with some z_1,\ldots, z_N\in\mathbb{C}. Now all z_1,\ldots, z_N are distinct.
Why is this claim true?
For example, if z_1=z_2, then (X-z_1)^2 divides p, but I see no reason to assume that (X-z_1)^2\in\mathbb{F}[X], so the claim remains a mystery to me.
<br /> p(X)=(X-z_1)\cdots (X-z_N)<br />
holds with some z_1,\ldots, z_N\in\mathbb{C}. Now all z_1,\ldots, z_N are distinct.
Why is this claim true?
For example, if z_1=z_2, then (X-z_1)^2 divides p, but I see no reason to assume that (X-z_1)^2\in\mathbb{F}[X], so the claim remains a mystery to me.