Problems & Puzzles:
Puzzle 838. Follow up to
puzzle 837 we asked for prime Kaprekar
numbers. Jan van Delden and Emmanuel Vantieghem demonstrated that
all prime repunits 1 mod 9 are Kaprekar numbers, but it could happen
that exist some prime Kaprekar numbers out of these prime repunits.
might exist prime divisors d of N =10^n - 1 that are not repunits but that satisfy d = 1 (mod N/d). These numbers would
be Kaprekar numbers when they are unitary divisors".
one (if the smallest the better) of these prime Kaprekar numbers
out of the prime repunits, or show that these do not exist for
some other reason.