3

Part of 2016 Azerbaijan JBMO TST

Problems(2)

Source: Morocco test

Find all the pime numbers

(p,q)

p^{3}+p=q^{2}+q

m*n table colored with white and black

Source: 2016 Azerbaijan JBMO TST, D2 P3

All cells of the

m\times n

table are colored either white or black such that all corner cells of any rectangle containing the cells of this table with sides greater than one cell are not the same color. For values

m = 2, 3, 4,

n

such that the mentioned coloring is possible.

combinatoricsColor problem