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2007 Swedish Mathematical Competition
1
1
Part of
2007 Swedish Mathematical Competition
Problems
(1)
diophantine system, xyzu-x^3=9 , x+yz=3/2 u
Source: 2007 Swedish Mathematical Competition p1
4/27/2021
Solve the following system
{
x
y
z
u
−
x
3
=
9
x
+
y
z
=
3
2
u
\left\{ \begin{array}{l} xyzu-x^3=9 \\ x+yz=\dfrac{3}{2}u \\ \end{array} \right.
{
x
yz
u
−
x
3
=
9
x
+
yz
=
2
3
u
in positive integers
x
x
x
,
y
y
y
,
z
z
z
and
u
u
u
.
number theory
Diophantine equation
system of equations
diophantine