Question 73
Determine all positive integers $n$ such that the (3-variable) polynomial
$$
P_n(x, y, z) = (x - y)^{2n}(y - z)^{2n} + (y - z)^{2n}(z - x)^{2n} + (z - x)^{2n}(x - y)^{2n}
$$
divides the (3-variable) polynomial
$$
Q_n(x, y, z) = [(x - y)^{2n} + (y - z)^{2n} + (z - x)^{2n}]^{2n}.
$$
$$
P_n(x, y, z) = (x - y)^{2n}(y - z)^{2n} + (y - z)^{2n}(z - x)^{2n} + (z - x)^{2n}(x - y)^{2n}
$$
divides the (3-variable) polynomial
$$
Q_n(x, y, z) = [(x - y)^{2n} + (y - z)^{2n} + (z - x)^{2n}]^{2n}.
$$