Question 122
For the real number sequence $\{a_n\}_{n=1}^{\infty}$, we are given that $a_1 = 1$, $a_2 = 3$, and for $n \ge 1$,
$$
a_{n+2} = a_{n+1} + \frac{3a_{n+1} - 1}{a_{n+1} - a_n}
$$
Prove that the terms of the sequence $\{a_n\}$ are natural numbers and find the term $a_{61}$.
(Otgonbayar Uuye)
$$
a_{n+2} = a_{n+1} + \frac{3a_{n+1} - 1}{a_{n+1} - a_n}
$$
Prove that the terms of the sequence $\{a_n\}$ are natural numbers and find the term $a_{61}$.
(Otgonbayar Uuye)