MathDB
Problems
Contests
National and Regional Contests
Moldova Contests
Moldova Team Selection Test
1999 Moldova Team Selection Test
15
$(x-y)(y-z)(z-x)=x+y+z$
$(x-y)(y-z)(z-x)=x+y+z$
Source: Moldova TST 1999
August 7, 2023
Problem Statement
Distinct integers
x
,
y
,
z
x,y,z{}
x
,
y
,
z
verify the relation
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
=
x
+
y
+
z
(x-y)(y-z)(z-x)=x+y+z
(
x
−
y
)
(
y
−
z
)
(
z
−
x
)
=
x
+
y
+
z
. Find the smallest possibile value of
∣
x
+
y
+
z
∣
|x+y+z|
∣
x
+
y
+
z
∣
.
Back to Problems
View on AoPS