The conversation between human and AI assistant.
What are the last two digits in [math]2^{2016}[/math]?
That's really interesting! Can you give me an example of a problem where knowledge of these patterns would be useful?
Sure! One example could be in cryptography or encryption, where you need to calculate large powers of numbers modulo some integer. If you know the pattern of the last digits of powers of the base number, you can quickly calculate the last digits of the powers you need, without having to compute the entire number. This can save a lot of time and computation power.