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India LIMIT
2020 LIMIT
2020 LIMIT Category 1
14
Cubic diophantine
Cubic diophantine
Source: LIMIT 2020 Cat 1 Obj P14
May 2, 2020
number theory
algebra
limit
Problem Statement
Let
(
m
,
n
)
(m,n)
(
m
,
n
)
be the pairs of integers satisfying
2
(
8
n
3
+
m
3
)
+
6
(
m
2
ā
6
n
2
)
+
3
(
2
m
+
9
n
)
=
437
2(8n^3+m^3)+6(m^2-6n^2)+3(2m+9n)=437
2
(
8
n
3
+
m
3
)
+
6
(
m
2
ā
6
n
2
)
+
3
(
2
m
+
9
n
)
=
437
. Find the sum of all possible values of
m
n
mn
mn
.
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