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)
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.