Question 178
Let $a$ and $b$ be two distinct positive integers having the same parity.
Prove that $\frac{a!+b!}{2^a}$ is not an integer (note: $n! = 1 \cdot 2 \cdot \dots \cdot n$, for any positive integer $n$).
Prove that $\frac{a!+b!}{2^a}$ is not an integer (note: $n! = 1 \cdot 2 \cdot \dots \cdot n$, for any positive integer $n$).