For any integer n \ge 2, let b_n be the least positive integer such that, for any integer N, m divides N whenever m divides the digit sum of N written in base b_n, for 2 \le m \le n. Find the integer nearest to \frac{b_{36}}{b_{25}}.
For any integer n \ge 2, let b_n be the least positive integer such that, for any integer N, m divides N whenever m divides the digit sum of N written in base b_n, for 2 \le m \le n. Find the integer nearest to \frac{b_{36}}{b_{25}}.