# Divide and conquer recurrence relation

I have divide and conquer problem and below is the recurrence relation for it \begin{align}t (n) &= a\cdot t (n/4) + O (n^2/\log(n)) + O(n^2)\\ t(n) &= a\cdot t (n/4) + O(n^2) \end{align} I solved this recurrence for different values of $$a$$. These are the solutions below
$$=\begin{cases}O(n^2),&\text{ for }a = 8\\ O(n^2 \log(n)),&\text{ for }a = 16\\ O(n^5/2),&\text{ for }a=32 \end{cases}$$

Do these solution always apply if $$n$$ is not power of $$4$$ and how can I justify it?

• Is the last case n^(5/2)? – gnasher729 Mar 23 at 14:23