The method you describe works if you recall that 823 ≡ -2 (mod 11). (Change the base, not the exponent.)
Hi, I am trying to work out what the remainder is when 823^823 is divided by 11. I know how to do it say if its 2^200 is divided by 7 where you find the remainder of 2^1 divided by 7 and 2^2 divided by 7 and find a recurring pattern and do it that way. That didnt seem to work with 823^823
Any ideas?
Thanks