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