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1999 Ukraine Team Selection Test
8
8
Part of
1999 Ukraine Team Selection Test
Problems
(1)
x^n + 2^n + 1 divides x^{n+1} +2^{n+1} +1
Source: Ukrainian TST 1999 p8
2/13/2020
Find all pairs
(
x
,
n
)
(x,n)
(
x
,
n
)
of positive integers for which
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
.
divides
number theory