A Polynomial Black Box

Algebra Level 3

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

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

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

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