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2023 pOMA
3
Two and a half variable diophantine
Two and a half variable diophantine
Source: pOMA 2023/3
November 21, 2023
Diophantine equation
number theory
Problem Statement
Find all positive integers
l
l
l
for which the equation
a
3
+
b
3
+
a
b
=
(
l
a
b
+
1
)
(
a
+
b
)
a^3+b^3+ab=(lab+1)(a+b)
a
3
+
b
3
+
ab
=
(
l
ab
+
1
)
(
a
+
b
)
has a solution over positive integers
a
,
b
a,b
a
,
b
.
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