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Putnam
1999 Putnam
2
Putnam 1999 A2
Putnam 1999 A2
Source:
December 22, 2012
Putnam
algebra
polynomial
college contests
Problem Statement
Let
p
(
x
)
p(x)
p
(
x
)
be a polynomial that is nonnegative for all real
x
x
x
. Prove that for some
k
k
k
, there are polynomials
f
1
(
x
)
,
f
2
(
x
)
,
…
,
f
k
(
x
)
f_1(x),f_2(x),\ldots,f_k(x)
f
1
(
x
)
,
f
2
(
x
)
,
…
,
f
k
(
x
)
such that
p
(
x
)
=
∑
j
=
1
k
(
f
j
(
x
)
)
2
.
p(x)=\sum_{j=1}^k(f_j(x))^2.
p
(
x
)
=
j
=
1
∑
k
(
f
j
(
x
)
)
2
.
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