2006 SMT/Algebra Problems/Problem 7
Problem
Find all solutions to , where
and
are nonzero digits, and
is an integer. (
and
are not necessarily distinct.)
Solution
Notice that . Therefore,
must be divisible by
. Since
is prime, either
or
must be a multiple of
. However, if
, then
, so we only need to consider when
. In this case,
, a solution, so the only solution is
.