(untitled) (Journal of Informatics and Mathematical Sciences, 2009)
In the February 2008 issue of The American Mathematical Monthly (115, Problems and Solutions, p. 166) the following question was proposed by Roger Cuculiere: Find all nondecreasing functions f from R to R such that f(x + f(y)) = f(f(x)) + f(y) for all real x an y (Problem 11345). In the present paper we establish the general Lebesgue measurable solution, monotonic solutions as well as a description of the general solution of the functional equation in question.