Given a large number $n$, check if it has a zero digit in base $b$. By large number I mean something like $2^{13579^{3597}}$ so direct computation of digits is not feasible.
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6$\begingroup$ If you have a way to compute this number modulo $b^k$, you can show it is has a zero by taking (hopefully) small values of $k$. For example your number has a zero digit in base 10, as can be seen by taking $k=8$. Of course this criterion is useless if the zeros are for some reason not equally distributed. $\endgroup$– François BrunaultOct 11, 2021 at 7:14
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