OPM 1994

Determine the smallest natural number that has exactly $1994$ divisors.

Consider in a square $[ABCD]$ a point $E$ on the side $AB$ , different from $A$ and $B$ . On the side $BC$ consider the point $F$ such that $\angle AED = \angle DEF$ . Prove that $EF = AE + FC$ .

Proce that number $$\underbrace{11...11}_{2n \, digits}-\underbrace{22 ... 22}_{n \, digits}$$ is, for every natural $n$ , a perfect square.