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7
Polynomial equations with floor
Polynomial equations with floor
Source: INAMO 2020 P7
October 14, 2020
algebra
polynomial
floor function
functional equation
Problem Statement
Determine all real-coefficient polynomials
P
(
x
)
P(x)
P
(
x
)
such that
P
(
⌊
x
⌋
)
=
⌊
P
(
x
)
⌋
P(\lfloor x \rfloor) = \lfloor P(x) \rfloor
P
(⌊
x
⌋)
=
⌊
P
(
x
)⌋
for every real numbers
x
x
x
.
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