  This article gives an alternative proof of the fact that
N_{Q(zeta)/Q}(1-zeta)=p where p is an odd prime number and zeta is a primitive
p-th root of unity, and uses it to prove that N_{Q(zeta)/Q}(1+zeta-zeta^2)=L(p)
the p-th Lucas number. It shows a relation between this result and a
generalisation of the Newman phenomenon.
