2023 IMO Problems/Problem 3

Problem

For each integer $k \geqslant 2$ , determine all infinite sequences of positive integers $a_1, a_2, \ldots$ for which there exists a polynomial $P$ of the form $P(x)=x^k+c_{k-1} x^{k-1}+\cdots+c_1 x+c_0$ , where $c_0, c_1, \ldots, c_{k-1}$ are non-negative integers, such that $P\left(a_n\right)=a_{n+1} a_{n+2} \cdots a_{n+k}$ for every integer $n \geqslant 1$ .

Solution

https://www.youtube.com/watch?v=JhThDz0H7cI [Video contains solutions to all day 1 problems] https://www.youtube.com/watch?v=SP-7LgQh0uY [Video contains solution to problem 3]

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2023 IMO Problems/Problem 3

Problem

Solution