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Solve the equation for x,y,z ∈ Z
Solve the equation for x,y,z ∈ Z
Source:
September 1, 2010
number theory
equation
IMO Shortlist
IMO Longlist
Problem Statement
Find all triples
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
of integers such that
1
x
2
+
2
y
2
+
3
z
2
=
2
3
\frac{1}{x^2}+\frac{2}{y^2}+\frac{3}{z^2} =\frac 23
x
2
1
+
y
2
2
+
z
2
3
=
3
2
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