MathDB
Problems
Contests
International Contests
Austrian-Polish
1994 Austrian-Polish Competition
5
Integer equation: ... = 1 - xyz
Integer equation: ... = 1 - xyz
Source: APMC 1994, problem 5
February 23, 2006
number theory unsolved
number theory
Problem Statement
Solve in integers the following equation
1
2
(
x
+
y
)
(
y
+
z
)
(
z
+
x
)
+
(
x
+
y
+
z
)
3
=
1
−
x
y
z
\frac{1}{2}(x + y)(y + z)(z + x) + (x + y + z)^3 = 1 - xyz
2
1
(
x
+
y
)
(
y
+
z
)
(
z
+
x
)
+
(
x
+
y
+
z
)
3
=
1
−
x
yz
.
Back to Problems
View on AoPS