MathDB
switching places of numbers in any permutation if their difference is p, or q

Source: IFYM - XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade,finals p8

November 13, 2022
combinatoricspermutations

Problem Statement

Let pp and qq be mutually prime natural numbers greater than 11. Starting with the permutation (1,2,...,n)(1, 2, . . . , n), in one move we can switch the places of two numbers if their difference is pp or qq. Prove that with such moves we can get any another permutation if and only if n≥p+q−1n \ge p + q - 1.
Back to ProblemsView on AoPS