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Pan-African Shortlist
2018 Pan-African Shortlist
N5
2018 PAMO Shortlist: Diophantine equation
2018 PAMO Shortlist: Diophantine equation
Source: 2018 Pan-African Shortlist - N5
May 6, 2019
number theory
Diophantine equation
Problem Statement
Find all quadruplets
(
a
,
b
,
c
,
d
)
(a, b, c, d)
(
a
,
b
,
c
,
d
)
of positive integers such that
(
1
+
1
a
)
(
1
+
1
b
)
(
1
+
1
c
)
(
1
+
1
d
)
=
4.
\left( 1 + \frac{1}{a} \right) \left( 1 + \frac{1}{b} \right) \left( 1 + \frac{1}{c} \right) \left( 1 + \frac{1}{d} \right) = 4.
(
1
+
a
1
)
(
1
+
b
1
)
(
1
+
c
1
)
(
1
+
d
1
)
=
4.
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