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Let a complex number alpha,alpha!=1, be ...

Let a complex number `alpha,alpha!=1,` be a root of the equation `z^(p+q)-z^p-z^q+1=0,where p ,q` are distinct primes. Show that either `1+alpha+alpha^2++alpha^(p-1)=0or1+alpha+alpha^2++alpha^(q-1)=0` , but not both together.

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