Exercise 20, § 2

Show that there exists no polynomial identity in 6 indeterminates

where $P, Q, R$ are three polynomials with coefficients in $\mathbf{Z}$ with respect to the indeterminates $X_i$ and $Y_i$. (Observe that $15 = 3.5$ cannot be written in the form $p^2 + q^2 + r^2$, where $p, q, r$ are integers.)