Playing with 64-tuples

Find the number of 64-tuples ( x 0 , , x 63 ) (x_0, \dots, x_{63})

such that x 0 , , x 63 x_0, \dots, x_{63} are distinct elements of { 1 , 2 , , 2017 } \left\{1, 2, \dots, 2017 \right\} and

x 0 + x 1 + 2 x 2 + 3 x 3 + + 63 x 63 x_0+x_1+2x_2+3x_3+\cdots+63x_{63}

is divisible by 2017 2017

If your answer is of the form n ! ( ( m n ) m ) n!\left(\displaystyle {m\choose n }- m\right)

where m , n m,n are positive integers

submit m n m-n


The answer is 1953.

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