Question 5
Let $a_1,a_2,\ldots$ be a sequence of positive numbers satisfying, for any positive integers $k,l,m,n$ such that $k+n=m+l$,
$$\frac{a_k+a_n}{1+a_ka_n}=\frac{a_m+a_l}{1+a_ma_l}.$$
Show that there exist positive numbers $b,c$ so that $b\le a_n\le c$ for any positive integer $n$.
$$\frac{a_k+a_n}{1+a_ka_n}=\frac{a_m+a_l}{1+a_ma_l}.$$
Show that there exist positive numbers $b,c$ so that $b\le a_n\le c$ for any positive integer $n$.