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2001 Swedish Mathematical Competition
5
p'(x)^2 = c p(x) p''(x)
p'(x)^2 = c p(x) p''(x)
Source: 2001 Swedish Mathematical Competition p5
March 21, 2021
algebra
polynomial
Problem Statement
Find all polynomials
p
(
x
)
p(x)
p
(
x
)
such that
p
′
(
x
)
2
=
c
p
(
x
)
p
′
′
(
x
)
p'(x)^2 = c p(x) p''(x)
p
′
(
x
)
2
=
c
p
(
x
)
p
′′
(
x
)
for some constant
c
c
c
.
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