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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
86
86
Part of
PEN A Problems
Problems
(1)
A 86
Source:
5/25/2007
Find all positive integers
(
x
,
n
)
(x, n)
(
x
,
n
)
such that
x
n
+
2
n
+
1
x^{n}+2^{n}+1
x
n
+
2
n
+
1
divides
x
n
+
1
+
2
n
+
1
+
1
x^{n+1}+2^{n+1}+1
x
n
+
1
+
2
n
+
1
+
1
.
inequalities
induction
Divisibility Theory