Question 76
a. Let $a$, $n$, $k$ be positive integers. Prove that $a^{4n+k}$ and $a^k$ have identical first (rightmost) digits in their decimal representations.
b. Find the first digit of the decimal representation of the number
$$
2^{1999} + 7^{1999} + 9^{1999}.
$$
b. Find the first digit of the decimal representation of the number
$$
2^{1999} + 7^{1999} + 9^{1999}.
$$