Standard +0.3 This is a straightforward proof by induction with a divisibility statement. The base case is trivial (n=1 gives 3^6 - 2^2 = 729 - 4 = 725 = 5×145), and the inductive step requires standard algebraic manipulation to factor out 5 from 3^{2(k+1)+4} - 2^{2(k+1)} using the hypothesis. While it requires careful algebra, it follows a well-practiced template with no novel insight needed, making it slightly easier than average.
Prove by induction that for all positive integers $n$
$$f(n) = 3^{2n+4} - 2^{2n}$$
is divisible by 5
[6]
\hfill \mbox{\textit{SPS SPS FM Pure 2023 Q5 [6]}}