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APMO
1989 APMO
2
Prove no solutions other than 0
Prove no solutions other than 0
Source: APMO 1989
March 10, 2006
LaTeX
modular arithmetic
number theory
greatest common divisor
number theory unsolved
Problem Statement
Prove that the equation
6
(
6
a
2
+
3
b
2
+
c
2
)
=
5
n
2
6(6a^2 + 3b^2 + c^2) = 5n^2
6
(
6
a
2
+
3
b
2
+
c
2
)
=
5
n
2
has no solutions in integers except
a
=
b
=
c
=
n
=
0
a = b = c = n = 0
a
=
b
=
c
=
n
=
0
.
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