if is divded by 2012, what is least value of n.

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- May 13th 2012, 06:34 AMsaravananbsfind the least number n.
if is divded by 2012, what is least value of n.

- May 13th 2012, 07:04 AMProve ItRe: find the least number n.
- May 13th 2012, 07:09 AMsaravananbsRe: find the least number n.
2012 divides what is least value of n.

- May 13th 2012, 07:23 AMProve ItRe: find the least number n.
It doesn't for any .

If then there is some value of such that

Clearly this means that 9 needs to be a factor of 2013. But for any number to be divisible by 9, its digits need to add to a multiple of 9.

2 + 0 + 1 + 3 = 6, which is not a multiple of 9.

So 2013 can not ever be a value for , and therefore 2012 can not ever divide . - May 13th 2012, 07:30 AMsaravananbsRe: find the least number n.
why can't

Quote:

9^n-1 / 2012 is equal to k (instead of 1)

- May 13th 2012, 07:36 AMProve ItRe: find the least number n.
- May 14th 2012, 03:28 AMSylvia104Re: Find the least number n
There may well be no solutions but this is what I've found so far.

The RHS and so must But must be even because is divisible by and Hence

Now Combining this with gives

So if there is a solution, we must have, at the very least, In fact, it is clear that (as for so you should really start by looking at (Thinking)