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2009 SDMO (Middle School)
3
3
Part of
2009 SDMO (Middle School)
Problems
(1)
Fractional Diophantine
Source: 2009 SDMO Middle School Problem 3
8/24/2016
Find all ordered pairs of positive integers
(
a
,
b
)
\left(a,b\right)
(
a
,
b
)
such that
1
a
+
a
b
+
1
a
b
=
1.
\frac{1}{a}+\frac{a}{b}+\frac{1}{ab}=1.
a
1
+
b
a
+
ab
1
=
1.