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I got the first part, but I'm having trouble showing that f(5n) is divisible by 5. Can anyone help me out? Thanks! --[[User:Kfox|-Kristen]] 22:49, 4 March 2009 (UTC) | I got the first part, but I'm having trouble showing that f(5n) is divisible by 5. Can anyone help me out? Thanks! --[[User:Kfox|-Kristen]] 22:49, 4 March 2009 (UTC) | ||
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| + | Since f(5n) = 5*f(n-4) + 3*f(n-5), evaluate the two parts of this separately. The first part will always be divisible by 5 since it is 5*stuff. The second part we can find via induction. We know that f(5)=5. This is our base case. f(10) = 5*stuff + 3*f(5). Since f(5) is divisible by 5, so will f(10). This is the crank. f(15) = 5*stuff + 3*f(10), etc. | ||
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| + | Stephanie | ||
Latest revision as of 19:20, 4 March 2009
I got the first part, but I'm having trouble showing that f(5n) is divisible by 5. Can anyone help me out? Thanks! ---Kristen 22:49, 4 March 2009 (UTC)
Since f(5n) = 5*f(n-4) + 3*f(n-5), evaluate the two parts of this separately. The first part will always be divisible by 5 since it is 5*stuff. The second part we can find via induction. We know that f(5)=5. This is our base case. f(10) = 5*stuff + 3*f(5). Since f(5) is divisible by 5, so will f(10). This is the crank. f(15) = 5*stuff + 3*f(10), etc.
Stephanie
