# Thread: Divisibility by 30

1. ## Divisibility by 30

Does any one want to try this. I spent hours on it.

prove that 30| n^9 - n.

2. I might take a crack at it, but don't want to duplicate your work. What have you tried?

Do you know how to use the Principle of Mathmatical Induction?
Can you state divisibility by 30 in any other way?

3. Originally Posted by karlito03
Does any one want to try this. I spent hours on it.

prove that 30| n^9 - n.

Without induction:

$\displaystyle n^9-n=n(n^8-1)=n(n^4-1)(n^4+1)=n(n^2-1)(n^2+1)(n^4+1)=n(n-1)(n+1)(n^2+1)(n^4+1)$.

Well, now just prove that the above is always divisible by 2, by 3 and by 5 and you're done.

Tonio

4. How about "without spoon-feeding"?

5. Originally Posted by TheChaz
How about "without spoon-feeding"?
Thank you Tonio, I thought of it this way, but I kept getting stocked at some point.
"TheChaz" try ur induction as you suggested it and then you tell me how u will feel!.

6. My reply wasn't a defense of induction for this problem (which you have apparently seen as inefficient!); it was a criticism of (possibly) keeping you from the problem solving process.