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Contests
National and Regional Contests
Saudi Arabia Contests
Saudi Arabia Pre-TST + Training Tests
2010 Saudi Arabia Pre-TST
2.1
2.1
Part of
2010 Saudi Arabia Pre-TST
Problems
(1)
x + y +z = 2010, x^2 + y^2 + z^2 - xy - yz - zx =3
Source: 2010 Saudi Arabia Pre-TST 2.1
12/28/2021
Find all triples
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of positive integers such that
{
x
+
y
+
z
=
2010
x
2
+
y
2
+
z
2
−
x
y
−
y
z
−
z
x
=
3
\begin{cases} x + y +z = 2010 \\x^2 + y^2 + z^2 - xy - yz - zx =3 \end{cases}
{
x
+
y
+
z
=
2010
x
2
+
y
2
+
z
2
−
x
y
−
yz
−
z
x
=
3
diophantine
system of equations
System
number theory