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October 20, 2014

October 20, 2014

Posted by **Candice** on Monday, October 22, 2012 at 9:20pm.

ThankS!

- Math -
**Steve**, Tuesday, October 23, 2012 at 5:18amcheck for n=1

2^3 - 3^1 = 8-3 = 5

assume for k:

2^(3k) - 3^k = 5m for some m

now plug in k+1

2^(3(k+1)) - 3^(k+1)

= 2^(3k+3) - 3^(k+1)

= 2^3 * 2^(2k) - 3*3^k

= 8*2^(3k) - 3*3^k

= 3*2^(3k) + 5*2^(3k) - 3*3^k

= 3(2^(3k) - 3^k) + 5*2^(3k)

= 3(5m) + 5*2^(3k)

which is a multiple of 5.

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