Power Tower Puzzle Problem!

1. Sep 7, 2006

phantasmagoriun

Consider an exponential tower of three thousand 7's.
What is the remainder when you divide the tower by 11?
Note that this notation means 7^(7^7) not (7^7)^7. So it's kinda like the Ackermann Function maybe?
The final answer must be given as a single integer in the range 0-10.

Anyone got any ideas???

2. Sep 7, 2006

CRGreathouse

Yes, like the Ackerman function, but that doesn't matter.

7 mod 11 = ?
7^2 mod 11 = ?
7^3 mod 11 = ?
7^4 mod 11 = ?
7^5 mod 11 = ?
7^6 mod 11 = ?
...