Problem

Source: China TST 2002 Quiz

Tags: algebra unsolved, algebra



Given that $ a_1=1$, $ a_2=5$, $ \displaystyle a_{n+1} = \frac{a_n \cdot a_{n-1}}{\sqrt{a_n^2 + a_{n-1}^2 + 1}}$. Find a expression of the general term of $ \{ a_n \}$.