The conversation between human and AI assistant.
What is the remainder when 2^468 is divided by 11?
That's interesting. Can you give me an example of this pattern for smaller numbers?
Sure. For example, the remainder when 2^6 is divided by 11 is 9, because 6 leaves a remainder of 1 when divided by 5, and the remainder of 2^1 is 2, which corresponds to 9 in the cycle. Similarly, the remainder when 2^7 is divided by 11 is 5, because 7 leaves a remainder of 2 when divided by 5, and the remainder of 2^2 is 4, which corresponds to 5 in the cycle.