Question 112
Let $M_{n}$ be the number of integers $N$ such that
(a) $0 \leq N \lt 10^{n}$;
(b) $N$ is divisible by $4$;
(c) The sum of the digits of $N$ is also divisible by $4$.
Prove that $M_{n} \neq 10^{n} / 16$ for all positive integers $n$.
(a) $0 \leq N \lt 10^{n}$;
(b) $N$ is divisible by $4$;
(c) The sum of the digits of $N$ is also divisible by $4$.
Prove that $M_{n} \neq 10^{n} / 16$ for all positive integers $n$.