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4
2017 Guts #4: Diophantine equation
2017 Guts #4: Diophantine equation
Source:
February 21, 2017
number theory
Diophantine equation
Problem Statement
Find the number of ordered triples of nonnegative integers
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
that satisfy
(
a
b
+
1
)
(
b
c
+
1
)
(
c
a
+
1
)
=
84.
(ab + 1)(bc + 1)(ca + 1) = 84.
(
ab
+
1
)
(
b
c
+
1
)
(
c
a
+
1
)
=
84.
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