Question 2
For each positive integer $n$, let $x_n=\binom{2n}{n}$.
(a) Prove that if $2017^k/2\lt n\lt 2017^k$ for some positive integer $k$, then $2017\mid x_n$.
(b) Find every integer $h>1$ for which there exist positive integers $N,T$ such that $x_{n+T}\equiv x_n\pmod h$ for all $n>N$.
(a) Prove that if $2017^k/2\lt n\lt 2017^k$ for some positive integer $k$, then $2017\mid x_n$.
(b) Find every integer $h>1$ for which there exist positive integers $N,T$ such that $x_{n+T}\equiv x_n\pmod h$ for all $n>N$.