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National and Regional Contests
PEN Problems
PEN Q Problems
6
6
Part of
PEN Q Problems
Problems
(1)
Q 6
Source:
5/25/2007
Prove that for a prime
p
p
p
,
x
p
−
1
+
x
p
−
2
+
⋯
+
x
+
1
x^{p-1}+x^{p-2}+ \cdots +x+1
x
p
−
1
+
x
p
−
2
+
⋯
+
x
+
1
is irreducible in
Q
[
x
]
\mathbb{Q}[x]
Q
[
x
]
.
algebra
polynomial
calculus
derivative
binomial coefficients
binomial theorem
Polynomials