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.

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