Posted by Maximillion Pegasus on Sunday, August 23, 2009 at 3:19pm.
Show that 27 x 23^n + 17 x 10^2n is divisible by 11 for all positive integers n. I know that modulos should aid in answering this problem,

Mathematics  bobpursley, Sunday, August 23, 2009 at 3:34pm
27= 2 mode 5
23= 2 mode 1
17= 1 mode 6
10^2n= 100^n
100= 1 mode 9
So the problem reduces to
5*1^n+6*1^n
=5+6
=11 
Mathematics  bobpursley, Sunday, August 23, 2009 at 3:51pm
oops,typo error.
100=9 mode 1 the rest is correct.