Problem A. 756. (September 2019)
A. 756. Find all functions \(\displaystyle f\colon \mathbb{R}\to \mathbb{R}\) (functions with domain \(\displaystyle \mathbb{R}\) and values from \(\displaystyle \mathbb{R}\)) which satisfy the following two conditions:
\(\displaystyle (i)\) \(\displaystyle f(x+1)=f(x)+1\);
\(\displaystyle (ii)\) \(\displaystyle f(x^2)=\big(f(x)\big)^2\).
(Based on a problem of Romanian Masters of Mathematics)
(7 pont)
Deadline expired on October 10, 2019.
Statistics:
19 students sent a solution. 7 points: Bán-Szabó Áron, Beke Csongor, Bukva Dávid, Csaplár Viktor, Füredi Erik Benjámin, Pooya Esmaeil Akhoondy, Shuborno Das, Tóth 827 Balázs, Weisz Máté. 6 points: Stomfai Gergely. 5 points: 2 students. 0 point: 7 students.
Problems in Mathematics of KöMaL, September 2019