Mathematical and Physical Journal
for High Schools
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Problem A. 557. (March 2012)

A. 557. Show that the positive integers can be coloured with three colours in such a way that the equation x+y=z2 has no solution (x,y,z) consisting of distinct numbers with the same colour.

(Kolmogorov's Cup, 2011; a problem by F. Petrov and I. Bogdanov)

(5 pont)

Deadline expired on April 10, 2012.


6 students sent a solution.
5 points:Ágoston Tamás, Janzer Olivér, Maga Balázs, Mester Márton, Omer Cerrahoglu, Strenner Péter.

Problems in Mathematics of KöMaL, March 2012