IMO 2022 Shortlist A5
Find all positive integers n ě 2 for which there exist n real numbers a1 ă ¨¨¨ ă an and a real number r ą 0 such that th...
Category: Algebra
Problem
Find all positive integers n ě 2 for which there exist n real numbers a1 ă ¨¨¨ ă an and a real number r ą 0 such that the 1 npn´1q differences aj ´ai for 1 ď i ă j ď n are equal, in some order, to the numbers r1 ,r2 ,...,r npn´1q . (Czech Republic)