Real numbers on a circle
Source: 2020 Caucasus Mathematical Olympiad Seniors Problem 6
March 16, 2020
number theory
Problem Statement
Morteza wishes to take two real numbers and , and then to arrange six pairwise distinct real numbers on a circle so that for each three consecutive numbers at least one of the two following conditions holds:
1) their sum equals
2) their product equals .
Determine if Morteza’s wish could be fulfilled.