Show that is divisible by 64 for integer n > 1
I suggest "proof by induction". If n= 2, we have which is obviously divisible by 64.
Now, assume that, for some k, is divisible by 64. That is, that for some integer m. Now look at . Now that is obviously divisible by 8 but 64? You would have to prove that is divisible by 8. That is . Is 1 less than a power of 9 always divisible by 8? 9- 1= 8, 81- 1= 80= 8(10), 729- 1= 728= 8(91), ...
Hmmm, looks like another proof by induction! As above it works for n= 1. Suppose that for some integers k and j. Then . Yes! That completes the proof!
Hello, mark1950!
Another inductive proof . . .
Verify , which is divisible by 64.Show that is divisible by 64 for integer
Assume
Add to both sides:
. . .
. .
. . . . . .
. . . . .
. . . . . .
. . . . .
We have proved .
. . The inductive proof is complete.
Please learn something from your other thread: http://www.mathhelpforum.com/math-he...sible-7-a.html