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2Examples201ExampleForarationalprimepandforanyintegern1notonlydoesxnp0nothavearootinQbutinfactthepolynomialxnpisirreducibleinQx202ExampleLetpbeaprimenumberConsiderthepthcycloto

2.Examples[2.0.1]Example:Forarationalprimep andforanyintegern1 notonlydoesxnp=0nothavearootinQ but infact thepolynomialxnpisirreducibleinQ[x].[2.0.2]Example:Letpbeaprimenumber.Considerthepthcycloto

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