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SMO 2024 Senior Round 1 Question 21

SMO · SMO 2024 Senior Round 1

Question 21

Let $P(x)=a_0+a_1x+a_2x^2+\cdots+a_nx^n$ be a polynomial with non-negative integer coefficients satisfying $0\le a_i\le17$ for all $i$. If $P(18)=367616$, find the value of $P(3)$.