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IMO Longlists
1976 IMO Longlists
30
30
Part of
1976 IMO Longlists
Problems
(1)
Show that(x-a)^kQ(x) has at least k+1 non zero coefficients
Source:
1/25/2011
Prove that if
P
(
x
)
=
(
x
ā
a
)
k
Q
(
x
)
P(x) = (x-a)^kQ(x)
P
(
x
)
=
(
x
ā
a
)
k
Q
(
x
)
, where
k
k
k
is a positive integer,
a
a
a
is a nonzero real number,
Q
(
x
)
Q(x)
Q
(
x
)
is a nonzero polynomial, then
P
(
x
)
P(x)
P
(
x
)
has at least
k
+
1
k + 1
k
+
1
nonzero coefficients.
algebra
polynomial
induction
integration
algebra unsolved