Mathematical and Physical Journal
for High Schools
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Problem A. 506. (April 2010)

A. 506. Prove that for every prime p, there exists a colouring of the positive integers with p-1 colours such that the colours of the numbers {a,2a,3a,...,(p-1)a} are pairwise different for every positive integer a.

(5 pont)

Deadline expired on May 10, 2010.


13 students sent a solution.
5 points:Backhausz Tibor, Bodor Bertalan, Éles András, Frankl Nóra, Janzer Olivér, Mester Márton, Nagy 235 János, Nagy 648 Donát, Somogyi Ákos, Szabó 928 Attila, Weisz Ágoston, Zsakó András.
4 points:Strenner Péter.

Problems in Mathematics of KöMaL, April 2010