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1
2017 Team #1: Polynomials with equal floors
2017 Team #1: Polynomials with equal floors
Source:
February 19, 2017
algebra
polynomial
Problem Statement
Let
P
(
x
)
P(x)
P
(
x
)
,
Q
(
x
)
Q(x)
Q
(
x
)
be nonconstant polynomials with real number coefficients. Prove that if
⌊
P
(
y
)
⌋
=
⌊
Q
(
y
)
⌋
\lfloor P(y) \rfloor = \lfloor Q(y) \rfloor
⌊
P
(
y
)⌋
=
⌊
Q
(
y
)⌋
for all real numbers
y
y
y
, then
P
(
x
)
=
Q
(
x
)
P(x) = Q(x)
P
(
x
)
=
Q
(
x
)
for all real numbers
x
x
x
.
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