Find a 13 digit positive integer N whose base ten representation consists entirely of 8s and 9s such that 2¹³ divides N.

8,898,989,989,888

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

Posted by Ady TZIDON on 2011-12-21 12:14:35