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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
1999 Moldova Team Selection Test
15
15
Part of
1999 Moldova Team Selection Test
Problems
(1)
$(x-y)(y-z)(z-x)=x+y+z$
Source: Moldova TST 1999
8/7/2023
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
∣
.