6. Given 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.
When $x$ is even, $x^{4} \equiv 0(\bmod 16)$;
When $x$ is odd, $x^{2} \equiv 1(\bmod 8), x^{4} \equiv 1(\bmod 16)$.
Therefore, $x_{i}^{4} \equiv 0$ or $1(\bmod 16)$.
Since $1599=15(\bmod 16)$, it follows that $n \geqslant 15$.
Also, $1599=5^{4}+12 \times 3^{4}+2 \times 1^{4}$, hence, 1599 can be expressed as the sum of the fourth powers of 15 integers.