Show that when you substitute $(3n + 1)^{2}$ for each occurrence of $n$ and $(3m + 1)^{2}$ for each occurrence of m in the right-hand side of the formula for the function $f (m, n)$ in question $31,$ you obtain a one-to-one polynomial function $Z \times Z \rightarrow Z.$ It is an open question whether there is a one-to-one polynomial function $Q \times Q \rightarrow Q.$
