Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 462. (March 2015)

K. 462. $\displaystyle a)$ $\displaystyle f$ is a function defined on the set of real numbers. Given that $\displaystyle f(a)-f(b)=f(a\cdot b)$ for all $\displaystyle a$ and $\displaystyle b$, find the value of $\displaystyle f(2015)$.

$\displaystyle b)$ Is there a function $\displaystyle g$ defined on the set of real numbers such that $\displaystyle g(a) - g(b) = 2\cdot g(a\cdot b) - 2$ for all $\displaystyle a$ and $\displaystyle b$?

(6 pont)

Deadline expired on April 10, 2015.

### Statistics:

 30 students sent a solution. 6 points: Agócs Katinka, Csuha Boglárka, Encz Koppány, Farkas Lilla, Fekete Balázs Attila, János Zsuzsa Anna, Koronczi Fanni, Kozma Dávid Márk, Nagy Marcell, Németh Csilla Márta, Paulovics Péter, Sisák László Sándor, Slenker Balázs, Sziráki Boglárka Tünde, Tamási Kristóf Áron, Veliczky Barnabás. 5 points: Ágoston Tamás, Kovács 124 Marcell, Kovács András, Páhoki Tamás, Pintér 345 Balázs, Szarka Álmos, Tóth 802 Máté. 4 points: 3 students. 3 points: 3 students. 0 point: 1 student.

Problems in Mathematics of KöMaL, March 2015