Solve recurrence relation $T(n)=n^{1/5}T(n^{4/5})+5n/4$.

Question

I am trying to solve this recurrence relation – $T(n)=n^{1/5}T(n^{4/5})+5n/4$. I can't use the master's method and the recursion tree method because of that $n^{1/5}$ term. I am trying to remove this term, so I tried doing substitution like $n^{1/5}=m$ but clearly this is not helping. Can anyone give any suggestions?

Thanks!

Answer 1

HINT: Dividing by $n$, you get:$$\frac{T(n)}n=\frac{T(n^{4/5})}{n^{4/5}}+\frac54.$$