  We answer a question of Drungilas-Dubickas in the affirmative under the
assumption of standard conjectures on smooth numbers in polynomial sequences.
This gives evidence against the "Dubickas Conjecture", which Ka\v{c}inskait\.e
and Laurin\v{c}ikas proved implies universality results for the Hurwitz
zeta-function with certain algebraic irrational parameters.
  Under these standard conjectures we also prove some results that confirms
observations of Worley relating to a problem of Cassels on the multiplicative
dependence of algebraic numbers shifted by integers.
