MathDB

4

Part of 2023 Regional Olympiad of Mexico West

Problems(1)

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

10/21/2024
Prove that you can pick 1515 distinct positive integers between 11 and 20232023, 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.
number theoryPerfect PowersPerfect powerPerfect Squareperfect cube