lean_workbook_plus_74092

Find positive integers $k$ and $m$ satisfying $f(k)+f(m)=293$ given the conditions:\na) $f(1)=1$ ,\nb) $3f(n) \cdot f(2n+1) = f(2n) \cdot [1 + 3f(n)]$ for all $n \in \mathbb N$ ,\nc) $f(2n)<6f(n)$ for all $n \in \mathbb N$ .