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# Fp1 proof by mathematical induction that a expression is divisible by an interger... watch

1. First you show that f(1) is divisible by the interger, then assume f(k) is divisible by the interger.

In my book, for proving f(k+1) is divisible by the interger, they show this in all the examples:

f(k+1) - f(k) = whatever those values are substituted in

does it have to be f(k+1) - f(k) since it doesn't seem to be divisible by the interger for some questions I'm doing. Can it instead be e.g. f(k+1) + f(k), or would that no longer be proof?
2. (Original post by perrytheplatypus)
First you show that f(1) is divisible by the interger, then assume f(k) is divisible by the interger.

In my book, for proving f(k+1) is divisible by the interger, they show this in all the examples:

f(k+1) - f(k) = whatever those values are substituted in

does it have to be f(k+1) - f(k) since it doesn't seem to be divisible by the interger for some questions I'm doing. Can it instead be e.g. f(k+1) + f(k), or would that no longer be proof?

Showing f(k+1)+f(k) is divisible by what ever (lets call it n) would work. Since f(k) is divisible by n, and you've show that f(k+1)+f(k) is divisble by n, then f(k+1) = "f(k+1)+f(k)" - f(k) would also be divisible by n; you would need to add that step to your working.

HOWEVER, f(k+1)-f(k) will also be divisible by n, so can you give an example where you think it isn't.
3. (Original post by ghostwalker)
Showing f(k+1)+f(k) is divisible by what ever (lets call it n) would work. Since f(k) is divisible by n, and you've show that f(k+1)+f(k) is divisble by n, then f(k+1) = "f(k+1)+f(k)" - f(k) would also be divisible by n; you would need to add that step to your working.

HOWEVER, f(k+1)-f(k) will also be divisible by n, so can you give an example where you think it isn't.
f(n)=7^n+4^n+1
divisible by 6

I get f(k+1) - f(k) = 6x7^k + 3x4^k

but 3 isn't divisible by 6, so I'm stuck.
4. (Original post by perrytheplatypus)
f(n)=7^n+4^n+1
divisible by 6

I get f(k+1) - f(k) = 6x7^k + 3x4^k

but 3 isn't divisible by 6, so I'm stuck.
But is divisible by 2, so is divisible by...
5. (Original post by nuodai)
But is divisible by 2, so is divisible by...
...I feel like such an idiot, but thanks.

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