(2) For which positive integers $k$, does the inequality $a^{k}+b^{k}+c^{k}+d^{k}-k a b c d \geqslant M_{k}$ hold for all real numbers $a, b, c, d$? Find the maximum possible value of $M_{k}$, and indicate when equality holds. (2004 Australian Mathematical Olympiad problem)
(2) Notice that, when $k$ is odd, because the selection of sufficiently large negative values for $a, b, c, d$ results in a sufficiently large negative value for $a^{k}+b^{k}+c^{k}+d^{k}-k a b c d$, such a number $M_{k}$ does not exist.

When $k=2$, taking $a=b=d=r$, we get $a^{2}+b^{2}+c^{2}+d^{2}-2 a b c d=4 r^{2}-2 r^{4}$.
For sufficiently large $r$, this also yields an arbitrarily large negative value. Therefore, such a number $M_{t}$ does not exist.

When $k$ is even and $k \geqslant 4$, taking $a=b=d=1$, we get $a^{k}+b^{k}+c^{k}+d^{k}-k a b c d=4-k$.
Similarly to (1), we have
$$a^{k}+b^{t}+c^{k}+d^{2}-k a b c d \geqslant 4-k$$

i.e.,
$$\frac{a^{k}+b^{k}+c^{k}+d^{k}+(k-4) \cdot 1^{k}}{k} \geqslant a b c d$$

The equality holds under the same conditions as in (1).