MathDB

Let

k>1

be a given positive integer. A set

S

of positive integers is called good if we can colour the set of positive integers in

k

colours such that each integer of

S

cannot be represented as sum of two positive integers of the same colour. Find the greatest

t

such that the set

S=\{a+1,a+2,\ldots ,a+t\}

is good for all positive integers

a

.
A. Ivanov, E. Kolev

Problem Statement