IMO 2008 Shortlist A1

Find all functions f : (0,∞) → (0,∞) such that f(p)2 + f(q)2 f(r2) + f(s2) = p2 + q2 r2 + s2 for all p,q,r,s > 0 with pq...

imomathematicsolympiadshortlistalgebra

IMO 2008 Shortlist A1

Category: Algebra

Problem

Find all functions f : (0,∞) → (0,∞) such that f(p)2

  • f(q)2 f(r2) + f(s2) = p2
  • q2 r2 + s2 for all p,q,r,s > 0 with pq = rs.