Problem A. 765. (December 2019)

A. 765. Find all functions \(\displaystyle f\colon \mathbb{R}\to\mathbb{R}\) which satisfy the following equality for all \(\displaystyle x,y\in \mathbb{R}\):

\(\displaystyle f(x)f(y)-f(x-1)-f(y+1)=f(xy)+2x-2y-4. \)

Proposed by Dániel Dobák, Budapest

(7 pont)

Deadline expired on January 10, 2020.

Statistics:

15 students sent a solution.
7 points:	Füredi Erik Benjámin, Jánosik Áron, Osztényi József, Seres-Szabó Márton, Sztranyák Gabriella, Tóth 827 Balázs, Weisz Máté.
6 points:	Beke Csongor.
4 points:	3 students.
3 points:	2 students.
2 points:	1 student.
1 point:	1 student.

Problems in Mathematics of KöMaL, December 2019