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Putnam
1969 Putnam
A1
A1
Part of
1969 Putnam
Problems
(1)
Putnam 1969 A1
Source: Putnam 1969
3/31/2022
Let
f
(
x
,
y
)
f(x,y)
f
(
x
,
y
)
be a polynomial with real coefficients in the real variables
x
x
x
and
y
y
y
defined over the entire
x
y
xy
x
y
-plane. What are the possibilities for the range of
f
(
x
,
y
)
?
f(x,y)?
f
(
x
,
y
)?
Putnam
algebra
polynomial