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India Pre-Regional Mathematical Olympiad
2019 India PRMO
8
Algebra Problem
Algebra Problem
Source:
August 11, 2019
algebra
Problem Statement
How many positive integers
n
n
n
are there such that
3
≤
n
≤
100
3 \leq n \leq 100
3
≤
n
≤
100
and
x
2
n
+
x
+
1
x^{2^{n}} + x + 1
x
2
n
+
x
+
1
is divisible by
x
2
+
x
+
1
x^2 + x + 1
x
2
+
x
+
1
?
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