Can you solve in a minute?

Problem:

Solution:

Yes I can!

First, note that we only need to find the unit digit, so we can use the binomial theorem to help us to get rid of a lot of noise

$264^n \% 10 = (260 + 4)^n \%10 = 4^n \% 10$.

Next, notice the unit digit pattern in power of 4s.

4
16
64
256

It is just alternating 4 and 6, so the answer unit digit of the first term is 6, and the second term is 4, so the final unit digit is just 0.

By the way, $264^{102} + 264^{103} =$

2672061284943160918522454763266223159532013534099073129065764495853122847577901956596137015881471742644503555582762443491090345356529962017230305249153860349231365381334758920717003765678148536467012213716576437712205080690644467304472055027010109440

It takes no time to compute this in python:

>> 264 ** 102 + 264 ** 103