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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
90
90
Part of
PEN A Problems
Problems
(1)
A 90
Source:
5/25/2007
Determine all pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
of positive integers with
y
∣
x
2
+
1
y \vert x^2 +1
y
∣
x
2
+
1
and
x
2
∣
y
3
+
1
x^2 \vert y^3 +1
x
2
∣
y
3
+
1
.
Divisibility Theory