Hey guys,

Im confused with this :s

Find the remainder in the range 0 to 999 when 7^(8^9) is divided by 1000

We're dealing with a huge power, and it confused me as to how I am supposed to work it out.

I could start with doing

7 = 7 mod 1000

7^2 = 49 mod 1000

7^3 = 343 mod 1000

7^4 = 401 mod 1000

and maybe work it out with multiples of them? But then again the number (8^9) is huge so it might not be practical.

I was thinking of using Fermats Little Theorem, but I am unsure as to where I should begin.

Any help would be appreciated!