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National and Regional Contests
PEN Problems
PEN S Problems
17
S 17
S 17
Source:
May 25, 2007
Miscellaneous Problems
Problem Statement
Determine the maximum value of
m
2
+
n
2
m^{2}+n^{2}
m
2
+
n
2
, where
m
m
m
and
n
n
n
are integers satisfying
m
,
n
∈
{
1
,
2
,
.
.
.
,
1981
}
m,n\in \{1,2,...,1981\}
m
,
n
∈
{
1
,
2
,
...
,
1981
}
and
(
n
2
−
m
n
−
m
2
)
2
=
1.
(n^{2}-mn-m^{2})^{2}=1.
(
n
2
−
mn
−
m
2
)
2
=
1.
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