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Czech-Polish-Slovak Match
2000 Czech and Slovak Match
4
4
Part of
2000 Czech and Slovak Match
Problems
(1)
P(x^4)P(x^3)P(x^2)P(x)+1 has no integer roots
Source: Czech and Slovak Match 2000 P4
10/1/2017
Let
P
(
x
)
P(x)
P
(
x
)
be a polynomial with integer coefficients. Prove that the polynomial
Q
(
x
)
=
P
(
x
4
)
P
(
x
3
)
P
(
x
2
)
P
(
x
)
+
1
Q(x) = P(x^4)P(x^3)P(x^2)P(x)+1
Q
(
x
)
=
P
(
x
4
)
P
(
x
3
)
P
(
x
2
)
P
(
x
)
+
1
has no integer roots.
algebra
polynomial
Integer Polynomial
integer root