In Pollard's rho algorithm for integer factorization, we use pseudorandom sequences of the form $x_{i+1}=f(x_i)$ and look at them$\mod{n}$ until we get a cycle. Utilizing the birthday paradox, we can expect a cycle$\mod{n}$ in $O(\sqrt{n})$ steps. Typical polynomials that are used are $f(x)=x^2+1$ and $f(x)=x^2-1$.
My question is - why isn't $f(x)=x^2$ used? Is it not random enough$\mod{n}$? And if so, why is that?