Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
Already signed up?
New to KöMaL?
I want the old design back!!! :-)

Problem A. 420. (February 2007)

A. 420. Find all functions f\colon (0,\infty)\to\mathbb{R} such that |f(x)-f(y)|\le|x-y| for all x,y>0 and there exist positive constants a, b, c satisfying


f(ax)+f\left(\frac{b}{x}\right) =f(cx)

for all x.

(Proposed by Edgár Dobribán, Cluj-Napoca (Romania))

(5 pont)

Deadline expired on March 19, 2007.


Statistics:

12 students sent a solution.
5 points:Dobribán Edgár, Gyenizse Gergő, Hujter Bálint, Kisfaludi-Bak Sándor, Kónya 495 Gábor, Lovász László Miklós, Nagy 224 Csaba, Nagy 235 János, Nagy 314 Dániel, Tomon István.
2 points:1 student.
0 point:1 student.

Problems in Mathematics of KöMaL, February 2007