MathDB
Problems
Contests
International Contests
IMO Shortlist
1981 IMO Shortlist
13
13
Part of
1981 IMO Shortlist
Problems
(1)
Determine P(n+1)
Source:
9/15/2010
Let
P
P
P
be a polynomial of degree
n
n
n
satisfying
P
(
k
)
=
(
n
+
1
k
)
−
1
for
k
=
0
,
1
,
.
.
.
,
n
.
P(k) = \binom{n+1}{k}^{-1} \qquad \text{ for } k = 0, 1, . . ., n.
P
(
k
)
=
(
k
n
+
1
)
−
1
for
k
=
0
,
1
,
...
,
n
.
Determine
P
(
n
+
1
)
.
P(n + 1).
P
(
n
+
1
)
.
algebra
polynomial
Polynomials
IMO Shortlist