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Baltic Way
2019 Baltic Way
7
7
Part of
2019 Baltic Way
Problems
(1)
Partition of {2,3,...,k} into two product free sets
Source: 2019 Baltic Way P7
11/18/2019
Find the smallest integer
k
≥
2
k \geq 2
k
≥
2
such that for every partition of the set \{2, 3,\hdots, k\} into two parts, at least one of these parts contains (not necessarily distinct) numbers
a
a
a
,
b
b
b
and
c
c
c
with
a
b
=
c
ab = c
ab
=
c
.
combinatorics