2021 OIM Problems/Problem 5

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Problem

For a finite set $C$ of integers, we define $S(C)$ to be the sum of the elements of $C$. Find two nonempty sets $A$ and $B$, whose intersection is empty and whose union is the set ${1, 2, \cdots , 2021}$, such that the product $S(A)S(B)$ is a perfect square.

Solution

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See also

https://olcoma.ac.cr/internacional/oim-2021/examenes