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Poland - Second Round
1986 Poland - Second Round
5
5
Part of
1986 Poland - Second Round
Problems
(1)
f(x)f(x + 3) = f(x^2 + x + 3)
Source: Polish MO Recond Round 1986 p5
9/9/2024
Prove that if the polynomial
f
f
f
which is not identical to zero satisfies for every real
x
x
x
the equality
f
(
x
)
f
(
x
+
3
)
=
f
(
x
2
+
x
+
3
)
,
f(x)f(x + 3) = f(x^2 + x + 3),
f
(
x
)
f
(
x
+
3
)
=
f
(
x
2
+
x
+
3
)
,
then it has no real roots .
algebra
polynomial