6

Part of 2018 Czech and Slovak Olympiad III A

Problems(1)

3-coloring of numbers 1, 2, ..., n

Source: Czech and Slovak Olympiad 2018, National Round, Problem 6

Determine the least positive integer

n

with the following property – for every 3-coloring of numbers

1,2,\ldots,n

there are two (different) numbers

a,b

of the same color such that

|a-b|

is a perfect square.

Combinatorial Number Theorynational olympiadcombinatoricsnumber theory