15 integers in (1 -2023) such that the sum of a few is not m^2, m^3, m^n
Source: 2023 Mathematics Regional Olympiad of Mexico West P4
October 21, 2024
number theoryPerfect PowersPerfect powerPerfect Squareperfect cube
Problem Statement
Prove that you can pick distinct positive integers between and , such that each one of them and the sum between some of them is never a perfect square, nor a perfect cube or any other greater perfect power.