5. Let $a$ and $b$ be natural numbers greater than 1, for which $\sqrt{a \sqrt{a \sqrt{a}}}=b$. What is the smallest possible value of the sum $a+b$?

Solve the problem independently. You have 150 minutes for solving. The use of notes, literature, or a pocket calculator is not allowed.

Mathematical Competition for High School Students in Slovenia

## Invitational Competition

March 28, 2003

## Problems for 2nd Year