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Sweden Contests
Swedish Mathematical Competition
1974 Swedish Mathematical Competition
4
4
Part of
1974 Swedish Mathematical Competition
Problems
(1)
q (x^2 - 2x ) = q(x-2 )^2
Source: 1974 Swedish Mathematical Competition p4
3/26/2021
Find all polynomials
p
(
x
)
p(x)
p
(
x
)
such that
p
(
x
2
)
=
p
(
x
)
2
p(x^2) = p(x)^2
p
(
x
2
)
=
p
(
x
)
2
for all
x
x
x
. Hence find all polynomials
q
(
x
)
q(x)
q
(
x
)
such that
q
(
x
2
−
2
x
)
=
q
(
x
−
2
)
2
q\left(x^2 - 2x\right) = q\left(x-2\right)^2
q
(
x
2
−
2
x
)
=
q
(
x
−
2
)
2
polynomial
algebra