IMO 2021 Shortlist A8
Determine all functions f : R ÑR that satisfy fpaq´fpbq ˘ fpbq´fpcq ˘ fpcq´fpaq ˘ “fpab2 bc2 ca2 q´fpa2 b b2 c c2 aq for...
Category: Algebra
Problem
Determine all functions f : R ÑR that satisfy
fpaq´fpbq ˘
fpbq´fpcq
˘fpcq´fpaq ˘ “fpab2bc2
ca2 q´fpa2 b b2
c `c2
aq
for all real numbers a,b,c. 6 Saint-Petersburg — Russia, 16th–24th July 2021