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Switzerland Contests
Switzerland - Final Round
2007 Switzerland - Final Round
9
9
Part of
2007 Switzerland - Final Round
Problems
(1)
(a^3 + 1)/( 2ab^2 + 1) is an integer
Source: Switzerland - 2007 Swiss MO Final Round p9
12/26/2022
Find all pairs
(
a
,
b
)
(a, b)
(
a
,
b
)
of natural numbers such that
a
3
+
1
2
a
b
2
+
1
\frac{a^3 + 1}{2ab^2 + 1}
2
a
b
2
+
1
a
3
+
1
is an integer.
number theory
Integer
divides
divisible