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2008 JBMO Shortlist
9
(4a + p)/b+\(4b + p)/a , a^2/b+b^2/a \in Z
(4a + p)/b+\(4b + p)/a , a^2/b+b^2/a \in Z
Source: JBMO 2008 Shortlist N9
October 14, 2017
JBMO
number theory
Problem Statement
Let
p
p
p
be a prime number. Find all positive integers
a
a
a
and
b
b
b
such that:
4
a
+
p
b
+
4
b
+
p
a
\frac{4a + p}{b}+\frac{4b + p}{a}
b
4
a
+
p
+
a
4
b
+
p
and
a
2
b
+
b
2
a
\frac{a^2}{b}+\frac{b^2}{a}
b
a
2
+
a
b
2
are integers.
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