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2017 AIME Problems
8
Eugene Oneginteger outputs of polynomial
Eugene Oneginteger outputs of polynomial
Source: 2017 AIME II #8
March 23, 2017
AIME
AIME I
AIME II
algebra
polynomial
Problem Statement
Find the number of positive integers
n
n
n
less than
2017
2017
2017
such that
1
+
n
+
n
2
2
!
+
n
3
3
!
+
n
4
4
!
+
n
5
5
!
+
n
6
6
!
1+n+\frac{n^2}{2!}+\frac{n^3}{3!}+\frac{n^4}{4!}+\frac{n^5}{5!}+\frac{n^6}{6!}
1
+
n
+
2
!
n
2
+
3
!
n
3
+
4
!
n
4
+
5
!
n
5
+
6
!
n
6
is an integer.
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