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3
Fractional Diophantine
Fractional Diophantine
Source: 2009 SDMO Middle School Problem 3
August 24, 2016
Problem Statement
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.
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