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88
88
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PEN H Problems
Problems
(1)
H 88
Source:
5/25/2007
(Leo Moser) Show that the Diophantine equation
1
x
1
+
1
x
2
+
⋯
+
1
x
n
+
1
x
1
x
2
⋯
x
n
=
1
\frac{1}{x_{1}}+\frac{1}{x_{2}}+\cdots+\frac{1}{x_{n}}+\frac{1}{x_{1}x_{2}\cdots x_{n}}= 1
x
1
1
+
x
2
1
+
⋯
+
x
n
1
+
x
1
x
2
⋯
x
n
1
=
1
has at least one solution for every positive integers
n
n
n
.
induction
number theory
Diophantine equation
Diophantine Equations