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Italy Contests
Italy TST
1995 Italy TST
1
1
Part of
1995 Italy TST
Problems
(1)
Easy x|yz-1, y|zx-1, z|xy-1
Source:
11/22/2010
Determine all triples
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of integers greater than
1
1
1
with the property that
x
x
x
divides
y
z
−
1
yz-1
yz
−
1
,
y
y
y
divides
z
x
−
1
zx-1
z
x
−
1
and
z
z
z
divides
x
y
−
1
xy-1
x
y
−
1
.
number theory proposed
number theory