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2015 Ukraine Team Selection Test
7
7
Part of
2015 Ukraine Team Selection Test
Problems
(1)
elements of AB form finite arithmetic progression, A or B has at most 3 elements
Source: Ukraine TST 2015 p7
5/2/2020
Let
A
A
A
and
B
B
B
be two sets of real numbers. Suppose that the elements of the set
A
B
=
{
a
b
:
a
∈
A
,
b
∈
B
}
AB = \{ab: a\in A, b\in B\}
A
B
=
{
ab
:
a
∈
A
,
b
∈
B
}
form a finite arithmetic progression. Prove that one of these sets contains no more than three elements
arithmetic sequence
Sets
Product
algebra