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Serbia Team Selection Test
1995 Yugoslav Team Selection Test
Problem 1
Problem 1
Part of
1995 Yugoslav Team Selection Test
Problems
(1)
rational number theory
Source: Yugoslav TST 1995 P1
5/27/2021
Determine all triples
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
of positive rational numbers with
x
≤
y
≤
z
x\le y\le z
x
≤
y
≤
z
such that
x
+
y
+
z
,
1
x
+
1
y
+
1
z
x+y+z,\frac1x+\frac1y+\frac1z
x
+
y
+
z
,
x
1
+
y
1
+
z
1
, and xyz are natural numbers.
number theory
rational number
rational
rational numbers