**21**
Shubhodip
**·**2011-08-10 05:28:18
What meets the eye at first look is 3^{l}\equiv 3^{m}\left ( mod 10^{4} \right ) and 3^{m}\equiv 3^{n}\left ( mod 10^{4} \right )

After this it should be solvable but i think i need more time.

**21**
Shubhodip
**·**2011-08-10 10:20:43
I have seen the solution. knew something i did not:)

The answer is 3003

Here goes a hint:

Prove that if a^{x}â‰¡1(mod m) with gcd(a,m) = 1 and d is the minimum number such that a^{d}â‰¡1(mod m) then d|x. Well, only the statement is required here. The proof of this is trivial by another result (which i knew).Still medium amount of work is left.

**11**
Devil
**·**2011-08-10 22:14:36
I've done this, so no need of the hint. It was actually from some qsns on Number Theory that I had asked kaymant sir to mail me when I was in class XII.