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Baltic Way
2015 Baltic Way
3
Algebra Polynomials
Algebra Polynomials
Source: Baltic Way 2015
November 8, 2015
algebra
polynomial
Problem Statement
Let
n
>
1
n>1
n
>
1
be an integer. Find all non-constant real polynomials
P
(
x
)
P(x)
P
(
x
)
satisfying , for any real
x
x
x
, the identy
P
(
x
)
P
(
x
2
)
P
(
x
3
)
⋯
P
(
x
n
)
=
P
(
x
n
(
n
+
1
)
2
)
P(x)P(x^2)P(x^3)\cdots P(x^n)=P(x^{\frac{n(n+1)}{2}})
P
(
x
)
P
(
x
2
)
P
(
x
3
)
⋯
P
(
x
n
)
=
P
(
x
2
n
(
n
+
1
)
)
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