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Putnam
2003 Putnam
1
Putnam 2003 B1
Putnam 2003 B1
Source:
June 23, 2011
Putnam
algebra
polynomial
linear algebra
matrix
function
vector
Problem Statement
Do there exist polynomials
a
(
x
)
a(x)
a
(
x
)
,
b
(
x
)
b(x)
b
(
x
)
,
c
(
y
)
c(y)
c
(
y
)
,
d
(
y
)
d(y)
d
(
y
)
such that
1
+
x
y
+
x
2
y
2
=
a
(
x
)
c
(
y
)
+
b
(
x
)
d
(
y
)
1 + xy + x^2y^2= a(x)c(y) + b(x)d(y)
1
+
x
y
+
x
2
y
2
=
a
(
x
)
c
(
y
)
+
b
(
x
)
d
(
y
)
holds identically?
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