Find a 13 digit positive integer N whose base ten representation consists entirely of 8s and 9s
such that 213 divides N.
it is easy to build up from 8, 88, 888, 9888 etc by adding an 8 or 9 (depending on the parity of the prev/2^n )in front of the previous string of 8s &9s .
proof: by induction.
Edited on December 22, 2011, 11:00 am