Stewart (2013) proved that the biggest prime divisor of the nth term of a Lucas sequence of integers grows quicker than n, answering famous questions of Erdős and Schinzel. In this note we obtain a fully explicit and, in a sense, uniform version of Stewart's result.
Let γ be an algebraic number of degree 2 and not a root of unity. In this note we show that there exists a prime ideal p of Q(γ) satisfying νp(γ n − 1) ≥ 1, such that the rational prime p underlying p grows quicker than n.
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