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