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PEN H Problems
21
H 21
H 21
Source:
May 25, 2007
quadratics
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Diophantine Equations
APMO
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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