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National and Regional Contests
PEN Problems
PEN A Problems
79
79
Part of
PEN A Problems
Problems
(1)
A 79
Source:
5/25/2007
Determine all pairs of integers
(
a
,
b
)
(a, b)
(
a
,
b
)
such that
a
2
2
a
b
2
−
b
3
+
1
\frac{a^{2}}{2ab^{2}-b^{3}+1}
2
a
b
2
−
b
3
+
1
a
2
is a positive integer.
Divisibility Theory