2017 Putnam B6

Find the number of ordered $64$-tuples $(x_0,x_1,\dots,x_{63})$ such that $x_0,x_1,\dots,x_{63}$ are distinct elements of $\{1,2,\dots,2017\}$ and

$$

x_0 + x_1 + 2x_2 + 3x_3 + \cdots + 63 x_{63}

$$

is divisible by 2017.

查找有序 $64$ 元组 $(x_0,x_1,\dots,x_{63})$ 的数量，使得 $x_0,x_1,\dots,x_{63}$ 是 $\{1,2,\dots,2017\}$ 的不同元素，并且

$$

x_0 + x_1 + 2x_2 + 3x_3 + \cdots + 63 x_{63}

$$

可以被2017整除。