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Problems
Contests
National and Regional Contests
Iran Contests
Iran MO (2nd Round)
2020 Iran MO (2nd Round)
P5
P5
Part of
2020 Iran MO (2nd Round)
Problems
(1)
Dividing a set into pairs
Source: Iran second round 2020 ,Day 2 ,P5
7/15/2020
Call a pair of integers
a
a
a
and
b
b
b
square makers , if
a
b
+
1
ab+1
ab
+
1
is a perfect square. Determine for which
n
n
n
is it possible to divide the set
{
1
,
2
,
…
,
2
n
}
\{1,2, \dots , 2n\}
{
1
,
2
,
…
,
2
n
}
into
n
n
n
pairs of square makers.
number theory
Perfect Square