IMO 2016 Shortlist A7

Denote by R the set of all real numbers. Find all functions f : R → R such that f(0) 6= 0 and f(x + y)2 = 2f(x)f(y) + ma...

imomathematicsolympiadshortlistalgebra

IMO 2016 Shortlist A7

Category: Algebra

Problem

Denote by R the set of all real numbers. Find all functions f : R → R such that f(0) 6= 0 and f(x + y)2 = 2f(x)f(y) + max{f(x2 ) + f(y2 ),f(x2

  • y2 )} for all real numbers x and y.