Effective lower bounds for |z^d minus an S-unit| and the greatest prime factor of the difference, both tending to infinity with z^d.
Tijdeman,On the maximal distance between integers composed of small primes, Compositio Math
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On the difference between perfect powers and integral $S$-units
Effective lower bounds for |z^d minus an S-unit| and the greatest prime factor of the difference, both tending to infinity with z^d.