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1997 Italy TST
1
very old problem
very old problem
Source: Italian TST 1997
May 5, 2017
algebra
Problem Statement
Let
x
,
y
,
z
,
t
x,y,z,t
x
,
y
,
z
,
t
be real numbers with
x
,
y
,
z
x,y,z
x
,
y
,
z
not all equal such that
x
+
1
y
=
y
+
1
z
=
z
+
1
x
=
t
.
x+\frac{1}{y}=y+\frac{1}{z}=z+\frac{1}{x}=t.
x
+
y
1
=
y
+
z
1
=
z
+
x
1
=
t
.
Find all possible values of
t
t
t
such that
x
y
z
+
t
=
0
xyz+t=0
x
yz
+
t
=
0
.
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