Part A: Show that there are infinitely many positive integers $a, b,$ and $k$ such that $$k = \frac{2a + b^2 + b + 1}{a^2 + ab}.$$ Part B: Prove $k = 3$ for all integers $a$ and $b$ found in part A.
I have discovered a recursive formula that generates infinitely many solutions (which is PART A). However, I don't know how to approach PART B. The recursive formula I discovered is: $a_1 = 1$, $b_1 = 0$, $a_2 = 3$, $b_2 = 10$, $a_n = 5a_{n-1} - a_{n-2} - 1$, $b_n = a_{n-1}$.