Question 163
For every positive integer $n$, let $x_n = C_{2n}^n$.
1. Show that if $\frac{2017^k}{2} \lt n \lt 2017^k$ for some positive integer $k$ then $x_n$ is a multiple of $2017$.
2. Find all positive integer $h \gt 1$ such that there exist positive integers $N, T$ such that for all $n \gt N$ then $(x_n)$ is a periodic sequence mod $h$ with period $T$.
1. Show that if $\frac{2017^k}{2} \lt n \lt 2017^k$ for some positive integer $k$ then $x_n$ is a multiple of $2017$.
2. Find all positive integer $h \gt 1$ such that there exist positive integers $N, T$ such that for all $n \gt N$ then $(x_n)$ is a periodic sequence mod $h$ with period $T$.