What is the Remainder of a 3000-Layer 7 Power Tower Divided by 11?

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The discussion centers on calculating the remainder of a 3000-layer exponential tower of 7's when divided by 11. The notation used indicates that the expression is 7 raised to the power of 7 raised to the power of 7, continuing for 3000 layers. Participants explore modular arithmetic, specifically calculating powers of 7 modulo 11 to derive the final answer, which must be a single integer between 0 and 10.

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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?
 
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phantasmagoriun said:
Anyone got any ideas?

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 = ?
...
 

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