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2014 Cuba MO
4
(a^2b + a) / ( a^2 + b) are integers
(a^2b + a) / ( a^2 + b) are integers
Source: 2014 Cuba 2.4
September 20, 2024
number theory
Integer
Problem Statement
Find all positive integers
a
,
b
a, b
a
,
b
such that the numbers
a
2
b
+
a
a
2
+
b
\frac{a^2b + a}{a^2 + b}
a
2
+
b
a
2
b
+
a
and
a
b
2
+
b
b
2
−
a
\frac{ab^2 + b}{b^2 - a}
b
2
−
a
a
b
2
+
b
are integers.
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