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National and Regional Contests
Poland Contests
Poland - Second Round
1958 Poland - Second Round
3
3
Part of
1958 Poland - Second Round
Problems
(1)
integer roots f(x) = ax^3 + bx^2 + cx + d
Source: Polish MO second round 1958 p3
8/29/2024
Prove that if the polynomial
f
(
x
)
=
a
x
3
+
b
x
2
+
c
x
+
d
f(x) = ax^3 + bx^2 + cx + d
f
(
x
)
=
a
x
3
+
b
x
2
+
c
x
+
d
with integer coefficients takes odd values for
x
=
0
x = 0
x
=
0
and
x
=
1
x = 1
x
=
1
, then the equation
f
(
x
)
=
0
f(x) = 0
f
(
x
)
=
0
has no integer roots.
algebra
polynomial