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National and Regional Contests
Mongolia Contests
Mongolian Mathematical Olympiad
2002 Mongolian Mathematical Olympiad
Problem 3
sets equal in terms of integral parameter
sets equal in terms of integral parameter
Source: Mongolian MO 2002 Teachers P3
April 9, 2021
parameterization
Problem Statement
Find all positive integer
n
n
n
for which there exist real number
a
1
,
a
2
,
…
,
a
n
a_1,a_2,\ldots,a_n
a
1
,
a
2
,
…
,
a
n
such that
{
a
j
−
a
i
∣
1
≤
i
<
j
≤
n
}
=
{
1
,
2
,
…
,
n
(
n
−
1
)
2
}
.
\{a_j-a_i|1\le i<j\le n\}=\left\{1,2,\ldots,\frac{n(n-1)}2\right\}.
{
a
j
−
a
i
∣1
≤
i
<
j
≤
n
}
=
{
1
,
2
,
…
,
2
n
(
n
−
1
)
}
.
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