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2019 NMTC Junior
6
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Source: NMTC 2019 Junior P6
November 2, 2019
algebra
Problem Statement
Find all positive integer triples
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
that satisfy the equation
x
4
+
y
4
+
z
4
=
2
x
2
y
2
+
2
y
2
z
2
+
2
z
2
x
2
ā
63.
x^4+y^4+z^4=2x^2y^2+2y^2z^2+2z^2x^2-63.
x
4
+
y
4
+
z
4
=
2
x
2
y
2
+
2
y
2
z
2
+
2
z
2
x
2
ā
63.
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