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Sum of all possible values of P(10)

Source: Bangladesh Mathematical Olympiad 2021 Problem 4

February 20, 2022
algebra

Problem Statement

P(x)P(x) is a polynomial in xx with non-negative integer coefficients. If P(1)=5P(1)=5 and P(P(1))=177P(P(1))=177, what is the sum of all possible values of P(10)P(10)?
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