Question 3
Solve for all functions $f:\mathbb R_{>0}\to\mathbb R_{>0}$ satisfying, for every $x,y>0$,
$$f(x)=f(f(f(x))+y)+f(xf(y))f(x+y).$$
Proposed by Hung-Hsun Hans Yu. Source: Evan Chen’s third-party solution notes; https://aops.com/community/p24774907. One point is a nonofficial editorial normalization; this essay requires manual grading.
$$f(x)=f(f(f(x))+y)+f(xf(y))f(x+y).$$
Proposed by Hung-Hsun Hans Yu. Source: Evan Chen’s third-party solution notes; https://aops.com/community/p24774907. One point is a nonofficial editorial normalization; this essay requires manual grading.