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Iran MO (2nd Round)
1989 Iran MO (2nd round)
2
Root of a polynomial
Root of a polynomial
Source:
November 28, 2010
algebra
polynomial
algebra unsolved
Problem Statement
Let
n
n
n
be a positive integer. Prove that the polynomial
P
(
x
)
=
x
n
n
!
+
x
n
−
1
(
n
−
1
)
!
+
.
.
.
+
x
+
1
P(x)= \frac{x^n}{n!}+\frac{x^{n-1}}{(n-1)!}+...+x+1
P
(
x
)
=
n
!
x
n
+
(
n
−
1
)!
x
n
−
1
+
...
+
x
+
1
Does not have any rational root.
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