Question 50
The sequence of positive integers $a_1, a_2, a_3, \dots$, for each integer $i \ge 3$ satisfies the equality
$$
a_{i+1} = a_i + \gcd(a_{i-1}, a_{i-2}).
$$
Prove that there exist positive integers $N$ and $M$ such that for each $n \ge N$ holds $a_{n+1} - a_n = M$. (Palina Chernikava)
$$
a_{i+1} = a_i + \gcd(a_{i-1}, a_{i-2}).
$$
Prove that there exist positive integers $N$ and $M$ such that for each $n \ge N$ holds $a_{n+1} - a_n = M$. (Palina Chernikava)