Question 55
Determine whether there exists an infinite sequence $a_1, a_2, a_3, \dots$ of positive integers which satisfies the equality
$$
a_{n+2} = a_{n+1} + \sqrt{a_{n+1} + a_n}
$$
for every positive integer $n$.
$$
a_{n+2} = a_{n+1} + \sqrt{a_{n+1} + a_n}
$$
for every positive integer $n$.