Question 25
Do there exist polynomials $p(x)$, $q(x)$, $r(x)$ such that
$$
p(x - y + z)^3 + q(y - z - 1)^3 + r(z - 2x + 1)^3 = 1
$$
for all $x$, $y$, $z$?
Do there exist polynomials $p(x)$, $q(x)$, $r(x)$ such that
$$
p(x - y + z)^3 + q(y - z - 1)^3 + r(z - x + 1)^3 = 1
$$
for all $x$, $y$, $z$?
$$
p(x - y + z)^3 + q(y - z - 1)^3 + r(z - 2x + 1)^3 = 1
$$
for all $x$, $y$, $z$?
Do there exist polynomials $p(x)$, $q(x)$, $r(x)$ such that
$$
p(x - y + z)^3 + q(y - z - 1)^3 + r(z - x + 1)^3 = 1
$$
for all $x$, $y$, $z$?