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Rioplatense Mathematical Olympiad, Level 3
2001 Rioplatense Mathematical Olympiad, Level 3
1
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Part of
2001 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
system in integers, a^2+b^2=5mn and m^2+n^2=5ab
Source: Rioplatense Olympiad 2001 level 3 P1
9/6/2018
Find all integer numbers
a
,
b
,
m
a, b, m
a
,
b
,
m
and
n
n
n
, such that the following two equalities are verified:
a
2
+
b
2
=
5
m
n
a^2+b^2=5mn
a
2
+
b
2
=
5
mn
and
m
2
+
n
2
=
5
a
b
m^2+n^2=5ab
m
2
+
n
2
=
5
ab
system of equations
number theory