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Baltic Way
1995 Baltic Way
1
System of equations
System of equations
Source: Baltic Way 1995
October 8, 2011
algebra
system of equations
number theory proposed
number theory
Problem Statement
Find all triples
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of positive integers satisfying the system of equations
{
x
2
=
2
(
y
+
z
)
x
6
=
y
6
+
z
6
+
31
(
y
2
+
z
2
)
\begin{cases} x^2=2(y+z)\\ x^6=y^6+z^6+31(y^2+z^2)\end{cases}
{
x
2
=
2
(
y
+
z
)
x
6
=
y
6
+
z
6
+
31
(
y
2
+
z
2
)
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