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2020 Korea National Olympiad
4
4
Part of
2020 Korea National Olympiad
Problems
(1)
m^2-5n^2 and m^2+5n^2 are both perfect squares
Source: 2020 Korea National Olympiad P4
11/21/2020
Find a pair of coprime positive integers
(
m
,
n
)
(m,n)
(
m
,
n
)
other than
(
41
,
12
)
(41,12)
(
41
,
12
)
such that
m
2
ā
5
n
2
m^2-5n^2
m
2
ā
5
n
2
and
m
2
+
5
n
2
m^2+5n^2
m
2
+
5
n
2
are both perfect squares.
number theory
Diophantine equation