The conversation between human and AI assistant.
What are the last two digits in [math]2^{2016}[/math]?
That's fascinating! Can you tell me more about patterns in powers of 2?
Certainly! There are many patterns you can observe in the powers of 2. For example, if you add up the digits of each power of 2, the sum repeats every seven powers: 2, 4, 8, 7, 5, 1, and then repeats again. There are also patterns in the binary representation of powers of 2, which are used in computer science and programming.