TITLE: How to know if a term is divisible by 10
QUESTION [9 upvotes]: I have some difficulties to solve this easy problem, could someone help me?
Is $4^{1000}-6^{500}$ divisible by $10$?

REPLY [6 votes]: $4^2 \equiv 6 \mod 10$
$\Rightarrow 4^{1000} \equiv 6^{500} \mod 10$