Question 2
Let $a_n,b_n$, $n=1,2,\ldots$, be two sequences of integers defined by $a_1=1,b_1=0$ and, for $n\ge1$,
$$a_{n+1}=7a_n+12b_n+6,\qquad b_{n+1}=4a_n+7b_n+3.$$
Prove that $a_n^2$ is the difference of two consecutive cubes.
$$a_{n+1}=7a_n+12b_n+6,\qquad b_{n+1}=4a_n+7b_n+3.$$
Prove that $a_n^2$ is the difference of two consecutive cubes.