The conversation between human and AI assistant.
What is the remainder when 2^468 is divided by 11?
That's interesting. How did you calculate that?
I used the Fermat's Little Theorem, which states that if p is a prime number, then for any integer a, the number a^p - a is an integer multiple of p. So in this case, 2^11 - 2 is an integer multiple of 11, and therefore 2^468 is equivalent to 2^(11x42) x 2^6, which is equal to (2^11 - 2)^42 x 2^6 (mod 11). This reduces to 2^6 (mod 11), which is equal to 64 (mod 11), which is equal to 1 (mod 11).