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and a given integer 
let 
denote the exponent of 
. Given 
and 
a set of 
primes, show that there are infinitely many positive integers 
for all 
.
I had a go at this question again but it yielded no results. None of the general number theory related theorems helped ...
I don't know if this helps at all, but apparently there is a formula due to Legendre saying that, where
is the sum of the digits of n in base p.
Reference: http://www.math.tulane.edu/~vhm/web_html/k-central.pdf (pdf file).
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