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1988 IMO Longlists
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93
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1988 IMO Longlists
Problems
(1)
Polynomial and binomial coefficient
Source: IMO LongList 1988, Vietnam 5, Problem 93 of ILL
11/9/2005
Given a natural number
n
,
n,
n
,
find all polynomials
P
(
x
)
P(x)
P
(
x
)
of degree less than
n
n
n
satisfying the following condition
∑
i
=
0
n
P
(
i
)
⋅
(
−
1
)
i
⋅
(
n
i
)
=
0.
\sum^n_{i=0} P(i) \cdot (-1)^i \cdot \binom{n}{i} = 0.
i
=
0
∑
n
P
(
i
)
⋅
(
−
1
)
i
⋅
(
i
n
)
=
0.
algebra
polynomial
algebra unsolved