MathDB
Problems
Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2013 Junior Balkan Team Selection Tests - Moldova
6
4xyz = x^4 + y^4 + z^4 + 1.
4xyz = x^4 + y^4 + z^4 + 1.
Source: 2013 Moldova JBMO TST p6
February 25, 2021
Diophantine equation
diophantine
number theory
Problem Statement
Determine all triplets of real numbers
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
that satisfy the equation
4
x
y
z
=
x
4
+
y
4
+
z
4
+
1
4xyz = x^4 + y^4 + z^4 + 1
4
x
yz
=
x
4
+
y
4
+
z
4
+
1
.
Back to Problems
View on AoPS