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2020 Chile National Olympiad
4
4
Part of
2020 Chile National Olympiad
Problems
(1)
x + y -z = 6 , x^3 + y^3 -z^3 = 414, diophantine
Source: 2020 Chile National Olympiad level 2 p4
10/22/2022
Determine all three integers
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
that are solutions of the system
x
+
y
−
z
=
6
x + y -z = 6
x
+
y
−
z
=
6
x
3
+
y
3
−
z
3
=
414
x^3 + y^3 -z^3 = 414
x
3
+
y
3
−
z
3
=
414
number theory
Diophantine equation
Diophantine Equations
diophantine
system of equations