It is known that there exist integers $x_{1}, x_{2}, \cdots, x_{n}$, satisfying $x_{1}^{4}-x_{2}^{4}-\cdots+x_{n}^{4}=1599$, then the minimum value of the positive integer $n$ is
(A) 14
(B) 15
(C) 16
(D) 1599
6. (B).

Notice that when $x$ is even, $x^{4} \equiv 0(\bmod 16)$, and when $x$ is odd, $x^{2} \equiv 1(\bmod 8)$, thus it can be known that $x^{4} \equiv 1(\bmod 16)$. Therefore, $r_{1}^{4} \equiv 0$ or $1(\bmod 16)$, and since $1599 \equiv 15(\bmod 16)$, it follows that $n \geqslant 15$. Furthermore, since $1599 = J^{4} + 12 \times 3^{4} + 2 \times 1^{4}$, it can be expressed as the sum of the fourth powers of 15 integers. Therefore, the smallest value is 15.