Date: Thu, 12 Jan 2006 23:46:28 +0000
Mime-Version: 1.0 (Produced by PhpWiki 1.3.11p1)
Content-Type: application/x-phpwiki;
  pagename=Tower%20of%20Power%20Solution;
  flags="";
  author=chris;
  version=2;
  lastmodified=1137109588;
  author_id=chris;
  markup=2;
  hits=72;
  charset=iso-8859-1
Content-Transfer-Encoding: binary

<pre>
 9^11 = 9 (mod 100), so we need to find 8^...^1 (mod 10).
 8^5 = 8 (mod 10), so we need to find 7^...^1 (mod 4).
 7^3 = 7 (mod 4), so we need to find 6^...^1 (mod 2), but this is clearly 0, so 7^...^1 = 1 (mod 4) ==>
 8^...^1 = 8 (mod 10) ==> 9^...^1 = 9^8 (mod 100) = 21 (mod 100).
</pre>