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Romania Contests
Romania National Olympiad
1996 Romania National Olympiad
2
cute and easy
cute and easy
Source: Romania 1996
August 31, 2005
algebra
polynomial
algebra proposed
Problem Statement
Find all polynomials
p
n
(
x
)
=
a
n
x
n
+
a
n
−
1
x
n
−
1
+
.
.
.
+
a
1
x
+
a
0
p_n(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0
p
n
(
x
)
=
a
n
x
n
+
a
n
−
1
x
n
−
1
+
...
+
a
1
x
+
a
0
(
n
≥
2
n\geq 2
n
≥
2
) with real and non-zero coeficients s.t.
p
n
(
x
)
−
p
1
(
x
)
p
2
(
x
)
.
.
.
p
n
−
1
(
x
)
p_n(x)-p_1(x)p_2(x)...p_{n-1}(x)
p
n
(
x
)
−
p
1
(
x
)
p
2
(
x
)
...
p
n
−
1
(
x
)
be a constant polynomial. ;)
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