Math Gold Medalist
Lor
2023 USAMO
Problem 2
Let be the set of positive real numbers. Find all functions such that, for all ,
Important Ideas in Functional Equations
x=y=1
x=1
y=1
f(1)=c
f(x+c)=f(x)+2
f(x+f(x))=xc+2
If x+c=xy then y=1+c/x
f(1+c/x)=c+2/x
c=2
2019 IMO Problem 1
Solution