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

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The discussion revolves around finding the remainder of a massive exponential tower of three thousand 7's when divided by 11. Participants explore the properties of modular arithmetic, specifically calculating powers of 7 modulo 11. The calculations reveal a repeating pattern in the powers of 7, which simplifies the problem. The final answer must be a single integer between 0 and 10, emphasizing the need for efficient computation methods. The conversation highlights the complexity of the problem while focusing on modular reduction techniques.
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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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