### IMO Shortlist 2017 problem A2

Kvaliteta:

Avg: 2.0Težina:

Avg: 6.0Let be a real number. Gugu has a napkin with ten distinct real numbers written on it, and he writes the following three lines of real numbers on the blackboard: In the first line, Gugu writes down every number of the form , where and are two (not necessarily distinct) numbers on his napkin. In the second line, Gugu writes down every number of the form , where and are two (not necessarily distinct) numbers from the first line. In the third line, Gugu writes down every number of the form , where are four (not necessarily distinct) numbers from the first line. Determine all values of such that, regardless of the numbers on Gugu's napkin, every number in the second line is also a number in the third line.

Source: https://www.imo-official.org/problems/IMO2017SL.pdf