Stewart's Theorem revisited: suppressing the norm $\pm 1$ hypothesis

Abstract: Let

g a m m a

be an algebraic number of degree

2

and not a root of unity. In this note we show that there exists a prime ideal

m a t h f r a k p

of

m a t h b b Q (g a m m a)

satisfying

u_{m} a t h f r a k p (g a m m a^{n} - 1) g e 1

, such that the rational prime

p

underlying

m a t h f r a k p

grows quicker than

n

.

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