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CIIM
2021 CIIM
2
2
Part of
2021 CIIM
Problems
(1)
Real equality in Poly...
Source: CIIM 2021 #2
10/30/2021
Let
r
>
s
r>s
r
>
s
be positive integers. Let
P
(
x
)
P(x)
P
(
x
)
and
Q
(
x
)
Q(x)
Q
(
x
)
be distinct polynomials with real coefficients, non-constant(s), such that
P
(
x
)
r
−
P
(
x
)
s
=
Q
(
x
)
r
−
Q
(
x
)
s
P(x)^r-P(x)^s=Q(x)^r-Q(x)^s
P
(
x
)
r
−
P
(
x
)
s
=
Q
(
x
)
r
−
Q
(
x
)
s
for every
x
∈
R
x\in \mathbb{R}
x
∈
R
. Prove that
(
r
,
s
)
=
(
2
,
1
)
(r,s)=(2,1)
(
r
,
s
)
=
(
2
,
1
)
.
algebra