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2015 ITAMO
4
All pairs of integers satisfying a^3+b^3+3ab=1
All pairs of integers satisfying a^3+b^3+3ab=1
Source: ITAMO 2015 P4
June 21, 2015
number theory proposed
ITAMO
number theory
Problem Statement
Determine all pairs of integers
(
a
,
b
)
(a, b)
(
a
,
b
)
that solve the equation
a
3
+
b
3
+
3
a
b
=
1
a^3 + b^3 + 3ab = 1
a
3
+
b
3
+
3
ab
=
1
.
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