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Problems
Contests
National and Regional Contests
PEN Problems
PEN H Problems
23
23
Part of
PEN H Problems
Problems
(1)
H 23
Source:
5/25/2007
Find all
(
x
,
y
,
z
)
ā
Z
3
(x,y,z) \in {\mathbb{Z}}^3
(
x
,
y
,
z
)
ā
Z
3
such that
x
3
+
y
3
+
z
3
=
x
+
y
+
z
=
3
x^{3}+y^{3}+z^{3}=x+y+z=3
x
3
+
y
3
+
z
3
=
x
+
y
+
z
=
3
.
inequalities
Diophantine Equations