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67
H 67
H 67
Source:
May 25, 2007
Diophantine Equations
Problem Statement
Is there a positive integer
m
m
m
such that the equation
1
a
+
1
b
+
1
c
+
1
a
b
c
=
m
a
+
b
+
c
\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{abc}= \frac{m}{a+b+c}
a
1
+
b
1
+
c
1
+
ab
c
1
=
a
+
b
+
c
m
has infinitely many solutions in positive integers
a
,
b
,
c
a, b, c \;
a
,
b
,
c
?
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