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.
Statistics:
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