2023 IOQM/Problem 21
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For n ∈ N , consider non-negative integer-valued functions f on {1, 2, . . . , n} satisfying f(i) ≥ f(j) for i > j and Pn i=1 (i + f(i)) = 2023 . Choose n such that Pn i=1 f(i) is the least. How many such functions exist in that case?
