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So to do part 1, you simply show that for n = 1, the value is indeed divisible by 11. That's just arithmetic. For part 2, you use (n+1) in place of n in the expression. Then you break it up in such a way that you can get the expression that had just n in it as a component. I'll show you what I mean:
What I want is to transform this into an expression that has (27)23^{n} + (17)10^{2n }in it.
Now you can see the original (27)23^{n} + (17)10^{2n} in there (which we know is divisible by 11) and you just have to show that the remaining terms are also divisible by 11. Cheers,
James, Use arithmetic modulo 11. Penny  


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