IMO 2017 Shortlist A8
Assume that a fun tion f : R Ñ R satis es the following ondition: For every x,y P R su h that fpxqy ˘ fpyqx ˘ ą 0, we ha...
Category: Algebra
Problem
Assume that a fun tion f : R Ñ R satis es the following ondition:
For every x,y P R su h that
fpxqy
˘ fpyqx
˘
ą 0, we have fpxqy “ fpyqx.
Prove that fpxq y ď fpyq x whenever x ą y.
(Netherlands) 6 IMO 2017, Rio de Janeiro
Combinatori s