let F be a field with char p. Let a, b be in the field, with a not equal b^p .(adsbygoogle = window.adsbygoogle || []).push({});

show that f(x) = x^p - a is irreducible

i was thinking to start by contradiction

assume f(x) is not irreducible....than f(x) = (x-a1)(x-a2)....(x-an)

where no a can be equal to a p th power of b.

in order for the polynomial to be irreducible i would need to check that every number smaller than p and which is not a pth power of some b, is not a root of f(x). I dont really know how to proceed from here...can anyone give me a hint.. or maybe suggest a different proof ?

thnx

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# Homework Help: Irreducible polynomial

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