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# FP1 Proof by Induction... [+ rep] watch

1. And finally I am stuck after 50 or so questions...
Can someone explain where I'm going wrong
Sorry I don't know how to use latex, but will bother to learn eventually...

Okay this is what I've done so far...

Prove that 8^n - 3^n is divisible by 5 [for all positive integers of n blah blah].

Let f(n) = 8^n - 3^n
When n = 1,
f(1) = 8 - 3 = 5, which is divisible by 5.
Therefore, f(n) is divisible exactly by 5 when n=1.

Assume the general statement is true when n=k i.e.:
f(k) = 8^k - 3^k is divisible by 5.

When n = k + 1
f(k+1) - f(k) = 8^(k+1) - 3^(k+1) - (8^k - 3^k)
= 8.8^k - 8^k - 3.3^k + 3^k
= 8^k(8 - 1) - [3.3^k - 3^k]
= 8^k(8-1) - [3^k(3 - 1)]
= 7.8^k - 2.3^k

Now where do I go from here!? Thanks!!
2. booooooooooooomp
3. ...= 5.8^k + 2.8^k - 2.3^k = 5.8^k + 2(8^k-3^k) = 5.8^k + 2f(k)
4. (Original post by Magician)
where did u get the 5 from?
As in 7.8^k = 5.8^k + 2.8^k.

Makes sense now.
5. (Original post by Magician)
where did u get the 5 from?
7.8^k = 5.8^k +2.8^k

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