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Austrian-Polish
2003 Austrian-Polish Competition
1
1
Part of
2003 Austrian-Polish Competition
Problems
(1)
p(x-1)p(x+1)= p(x^2-1) polynomial
Source: Austrian Polish 2003 APMC
4/25/2020
Find all real polynomials
p
(
x
)
p(x)
p
(
x
)
such that
p
(
x
−
1
)
p
(
x
+
1
)
=
p
(
x
2
−
1
)
p(x-1)p(x+1)= p(x^2-1)
p
(
x
−
1
)
p
(
x
+
1
)
=
p
(
x
2
−
1
)
.
polynomial
functional
algebra
functional equation