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PEN Problems
PEN O Problems
5
O 5
O 5
Source:
May 25, 2007
Problem Statement
Let
M
M
M
be a positive integer and consider the set
S
=
{
n
∈
N
∣
M
2
≤
n
<
(
M
+
1
)
2
}
.
S=\{n \in \mathbb{N}\; \vert \; M^{2}\le n <(M+1)^{2}\}.
S
=
{
n
∈
N
∣
M
2
≤
n
<
(
M
+
1
)
2
}
.
Prove that the products of the form
a
b
ab
ab
with
a
,
b
∈
S
a, b \in S
a
,
b
∈
S
are distinct.
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