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guessing a polynomial (Serbia MO 2006 1st Grade P4)

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April 10, 2021
algebrapolynomial

Problem Statement

Tatjana imagined a polynomial P(x)P(x) with nonnegative integer coefficients. Danica is trying to guess the polynomial. In each step, she chooses an integer kk and Tatjana tells her the value of P(k)P(k). Find the smallest number of steps Danica needs in order to find the polynomial Tatjana imagined.
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