A Polynomial Black Box

Algebra Level 3

The polynomial p(x)p(x) is of degree 2017 and has non-negative integer coefficients which you don't know.

If you input a value like x=x0,x= x_0, the computer will output the value p(x0)p(x_0) at a cost of $1.

If you want to determine all 2018 coefficients of p(x)p(x) at a minimum cost using only positive integer inputs, what is your cost in dollars?

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