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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2023 Moldova Team Selection Test
11
11
Part of
2023 Moldova Team Selection Test
Problems
(1)
if $m+n\in A$ then $m\cdot n\in A.$
Source: Moldova TST 2023
4/9/2023
Find all sets
A
A
A
of nonnegative integers with the property: if for the nonnegative intergers
m
m
m
and
n
n
n
we have
m
+
n
∈
A
m+n\in A
m
+
n
∈
A
then
m
⋅
n
∈
A
.
m\cdot n\in A.
m
⋅
n
∈
A
.
combinatorics