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Austrian-Polish
1988 Austrian-Polish Competition
1
1
Part of
1988 Austrian-Polish Competition
Problems
(1)
Q(x) = P(x) +12, integer polynomials
Source: Austrian Polish 1988 APMC
4/30/2020
Let
P
(
x
)
P(x)
P
(
x
)
be a polynomial with integer coefficients. Show that if
Q
(
x
)
=
P
(
x
)
+
12
Q(x) = P(x) +12
Q
(
x
)
=
P
(
x
)
+
12
has at least six distinct integer roots, then
P
(
x
)
P(x)
P
(
x
)
has no integer roots.
Integer Polynomial
polynomial
Integers
algebra