Question 85
Let $\lfloor x\rfloor$ be the largest integer less than or equal to $x$. Let $n \in \mathbb{N}, n \geq 7$ be given.
Prove that $\binom{n}{7}-\left\lfloor\frac{n}{7}\right\rfloor$ is divisible by 7.
Prove that $\binom{n}{7}-\left\lfloor\frac{n}{7}\right\rfloor$ is divisible by 7.