Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

Already signed up?
New to KöMaL?

Problem A. 565. (May 2012)

A. 565. The positive integers are coloured with a finite number of colours. A function f from the set of positive integers to itself has the following two properties:

(a) if x $\le$ y, then f(x) $\le$ f(y); and

(b) if x, y, and z are (not necessarily distinct) positive integers of the same colour and x+y=z, then f(x)+f(y)=f(z).

Does it follow that the function $\frac{f(x)}x$ is bounded from above?

(Based on Romanian Master in Mathematics, problem 2012/3)

(5 pont)

Deadline expired on June 11, 2012.

Statistics:

0 student sent a solution.

Problems in Mathematics of KöMaL, May 2012