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Putnam
1971 Putnam
A4
A4
Part of
1971 Putnam
Problems
(1)
Putnam 1971 A4
Source:
4/6/2022
Show that for
0
<
ϵ
<
1
0 <\epsilon <1
0
<
ϵ
<
1
the expression
(
x
+
y
)
n
(
x
2
−
(
2
−
ϵ
)
x
y
+
y
2
)
(x+y)^n(x^2-(2-\epsilon)xy+y^2)
(
x
+
y
)
n
(
x
2
−
(
2
−
ϵ
)
x
y
+
y
2
)
is a polynomial with positive coefficients for
n
n
n
sufficiently large and integral. For
ϵ
=
.
002
\epsilon =.002
ϵ
=
.002
find the smallest admissible value of
n
n
n
.
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