MathDB
NT game with common multiples

Source: Kvant Magazine No. 3 2021 M2645

March 9, 2023
number theoryKvant

Problem Statement

Vitya wrote down nn{} different natural numbers in his notebook. For each pair of numbers from the notebook, he wrote out their smallest common multiple on the board. Could it happen for some n>100n>100 that n(nāˆ’1)/2n(n-1)/2 numbers on the board are (in some order) consecutive terms of a non-constant arithmetic progression?
Proposed by S. Berlov