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