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German National Olympiad
2022 German National Olympiad
4
4
Part of
2022 German National Olympiad
Problems
(1)
An Old-Style Cubic Diophantine Equation
Source: Germany 2022, Problem 4
6/25/2022
Determine all
6
6
6
-tuples
(
x
,
y
,
z
,
u
,
v
,
w
)
(x,y,z,u,v,w)
(
x
,
y
,
z
,
u
,
v
,
w
)
of integers satisfying the equation
x
3
+
7
y
3
+
49
z
3
=
2
u
3
+
14
v
3
+
98
w
3
.
x^3+7y^3+49z^3=2u^3+14v^3+98w^3.
x
3
+
7
y
3
+
49
z
3
=
2
u
3
+
14
v
3
+
98
w
3
.
number theory
number theory proposed
Diophantine equation
Diophantine Equations
cubic equation