 A f(x) = f(g(x)) + f(h(x)) - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: A f(x) = f(g(x)) + f(h(x)) (/showthread.php?tid=941) A f(x) = f(g(x)) + f(h(x)) - tommy1729 - 12/10/2014 Together with my friend mick We came to consider the following ( after thinking about fake function theory ) : Let a given A be 0 < A < 2. tommy-mick 3 entires Conjecture : For any real entire f(x) there exist real entire g(x) and h(x) such that A f(x) = f(g(x)) + f(h(x)) or A f(x) = f(g(x)) - f(h(x)) is satisfied. The idea of positive derivatives and the alike led to many disputes ( and related to fake function theory naturally ) Im tempted to mention that I considered some matrix ideas such as Carleman and some ideas from Gottfried. ( Though the ideas I tried based on Gottfried's ideas seem to have trouble with convergeance ... ) But with no result so far. Its possible that I posted this before in the past and maybe it has been considered 100 years ago. I believe the real intresting things happen when we develop ( or rediscover ) the tools to solve this. This is because this problem is a cornerstone ; many numerical methods and theoretical ideas I had - but did not publish - depend on the truth of this and a way to compute it. Bye the way you can vote for mick on MSE , he put himself as a candidate for moderator. Since he is probably the only young MSE user into tetration with a rep above 2000 he might be the man ( boy ) to defend/judge tetration Q&A. My apologies if im wrong : maybe some other users here or on MSE are young and have rep above 2000 too. ( Sheldon and Gottfried are on MSE but they are older , perhaps im forgetting balarka or galathaea or ... ) regards tommy1729