SOLUTION: show that 27 * 23^n + 17 * 10^2n is divisible by 11 for all positive integers n.

Question 892508: show that 27 * 23^n + 17 * 10^2n is divisible by 11 for all positive integers n.

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Proof by induction.
For n = 1: . 2321/11 = 211.
Induction hypothesis: Let the statement be true for n = k: Let
be divisible by 11.
To show: is divisible by 11.

=
=
=
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Since the first grouped term is divisible by 11 by the induction hypothesis, and the second grouped term has 11 as a factor, divisibility of by 11 follows.
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