Done ($a=b=1$ satisfy $a\not =0,b>0,a+b\not =1$)

Reviewing old problems, any solutions here???

N.T.TUAN wrote: Find all continuous functions $f : \mathbb{R}\to\mathbb{R}$ such that for all $x \in\mathbb{ R}$, \[f (f (x)) = f (x)+x.\] See http://artofproblemsolving.com/community/c6h1344617p7316804 subcase 7.1.1

Thank you!!