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National and Regional Contests
PEN Problems
PEN A Problems
109
109
Part of
PEN A Problems
Problems
(1)
A 109
Source:
5/25/2007
Find all positive integers
a
a
a
and
b
b
b
such that
a
2
+
b
b
2
−
a
and
b
2
+
a
a
2
−
b
\frac{a^{2}+b}{b^{2}-a}\text{ and }\frac{b^{2}+a}{a^{2}-b}
b
2
−
a
a
2
+
b
and
a
2
−
b
b
2
+
a
are both integers.
Divisibility Theory