Problem - 274
Find the remainder when $3^{2019} + 4^{2019}$ is divided by 5?
Answer
1
$$3^{2019} + 4^{2019}\equiv (3^2)^{1009}\times 3 + (-1)^{2019}\equiv(-1)^{1009}\times 3 -1 \equiv \boxed{1}\pmod{5}$$