MathDB

Let

k>1

be a positive integer. A set

S{}

is called good if there exists a colouring of the positive integers with

k{}

colours, such that no element from

S{}

can be written as the sum of two distinct positive integers having the same colour. Find the greatest positive integer

t{}

(in terms of

k{}

) for which the set

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

is good, for any positive integer

a{}

Problem Statement