2023 IMO Problems/Problem 3
Problem
For each integer , determine all infinite sequences of positive integers for which there exists a polynomial of the form , where are non-negative integers, such that for every integer .
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]
https://www.youtube.com/watch?v=CmJn5FKxpPY [Video contains another solution to problem 3]
Let and be functions of positive integers n and i respectively.
Let , then ,
Let