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Dutch Mathematical Olympiad
2002 Dutch Mathematical Olympiad
2
2
Part of
2002 Dutch Mathematical Olympiad
Problems
(1)
diophantine (1+1/x)(1+1/y)(1+1/z) = 3
Source: Dutch NMO 2002 p2
9/21/2019
Determine all triplets
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
of positive integers with
x
≤
y
≤
z
x \le y \le z
x
≤
y
≤
z
that satisfy
(
1
+
1
x
)
(
1
+
1
y
)
(
1
+
1
z
)
=
3
\left(1+\frac1x \right)\left(1+\frac1y \right)\left(1+\frac1z \right) = 3
(
1
+
x
1
)
(
1
+
y
1
)
(
1
+
z
1
)
=
3
number theory
Diophantine equation
diophantine