I'm having a lot of trouble figuring out this discrete math question:
What are the last four bits in the binary expansion of 1234^5555 + 4321 ^5555?
I need to add the two numbers and convert to binary. From what I know so far, to get the last bit from binary, you need to take mod 2. From this, to get the last four bits I understand that you need to take mod 16. However, I don't know how to efficiently take a mod of a very large number or convert a large number to binary.
I've also considered using Fermat's Little Theorem.
Can someone help me out or guide me along the right path?