MathDB

Let

M \ge 3

be an integer and let S \equal{} \{3,4,5,\ldots,m\}. Find the smallest value of

m

such that for every partition of

S

into two subsets, at least one of the subsets contains integers

a

b

, and

c

(not necessarily distinct) such that ab \equal{} c.
Note: a partition of

S

is a pair of sets

A

B

such that A \cap B \equal{} \emptyset, A \cup B \equal{} S.

Problem Statement