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Divisibility problem with fractions
Divisibility problem with fractions
Source: IMOTC 2015 Practice Test 1 Problem 1
July 11, 2015
number theory
APMO
Problem Statement
Find all positive integers
a
,
b
a,b
a
,
b
such that
a
2
+
b
b
2
−
a
\frac{a^2+b}{b^2-a}
b
2
−
a
a
2
+
b
and
b
2
+
a
a
2
−
b
\frac{b^2+a}{a^2-b}
a
2
−
b
b
2
+
a
are also integers.
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