Hi all, here is a little challenge for you all, involving number theory.

Good luckLet $\displaystyle a_{n + 1} \equiv {a_n}^3 \pmod{113}$, $\displaystyle a_1$ being the initial term.

If I tell you that $\displaystyle a_4 = 26$, can you find $\displaystyle a_1$ ?

Please don't just try all possible values ...