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Problems
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National and Regional Contests
PEN Problems
PEN H Problems
44
44
Part of
PEN H Problems
Problems
(1)
H 44
Source:
5/25/2007
For all
n
ā
N
n \in \mathbb{N}
n
ā
N
, show that the number of integral solutions
(
x
,
y
)
(x, y)
(
x
,
y
)
of
x
2
+
x
y
+
y
2
=
n
x^{2}+xy+y^{2}=n
x
2
+
x
y
+
y
2
=
n
is finite and a multiple of
6
6
6
.
calculus
integration
Diophantine Equations