Question 187
Let $r$ be a positive integer and let $N_r$ be the smallest positive integer such that the numbers
$$
\frac{N_r}{n+r} \binom{2n}{n}, \quad n = 0, 1, 2, \dots,
$$
are all integers. Show that
$$
N_r = \frac{r}{2} \binom{2r}{r}.
$$
$$
\frac{N_r}{n+r} \binom{2n}{n}, \quad n = 0, 1, 2, \dots,
$$
are all integers. Show that
$$
N_r = \frac{r}{2} \binom{2r}{r}.
$$