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Sum of powers of integers less or equal 2023

Source: Cono Sur 2023 #1

August 7, 2023
inequalitiesSum of powerscono sur

Problem Statement

A list of nn positive integers a1,a2,a3,…,ana_1, a_2,a_3,\ldots,a_n is said to be good if it checks simultaneously: ∙a1<a2<a3<⋯<an,\bullet a_1<a_2<a_3<\cdots<a_n, ∙a1+a22+a33+⋯+ann≤2023.\bullet a_1+a_2^2+a_3^3+\cdots+a_n^n\le 2023. For each n≥1n\ge 1, determine how many good lists of nn numbers exist.
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