The hint for this problem is $a^{n+1} - 1 = (a + 1)(a^n - 1) - a(a^{n-1} - 1)$
I see that the problem is true because if you distribute the $a$ and the $-1$ the terms cancel out to equal the left side. However, since it is telling me to use strong induction I am guessing there is more I am supposed to be doing. On the hint I can see that it is a true statement, but I am not sure how to use that to prove the equation or how the right side of the hint relates to the right side of the problem. Also, I do realize that in the case of the hint $n = 1$ would be the special case.