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 
.
