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From Chapter VII of Lang's Algebra.

The question asks if $n\geq 6$ and $n$ is divisible by at least two primes, show that $1-\zeta$ is a unit in the ring $\mathbb{Z}[\zeta]$

I am having a hard time understanding why this is true. This is in the integral dependence chapter, but that has not given me any inspiration. I have also tried using cyclotonic polynomial to no avail

Thanks for any direction.

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    Looking at concrete examples often helps. $n=6$ is small enough that maybe it's not too hard to find an explicit inverse, assuming one exists. I bet finding the inverse will suggest a general form. On a different note, my first instinct is to find the norm.2012-10-18

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