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1990 Putnam
B5
B5
Part of
1990 Putnam
Problems
(1)
alpha_i such that polynomial has all real/distinct roots
Source: 1990 Putnam B5
7/12/2013
Is there an infinite sequence
a
0
,
a
1
,
a
2
,
⋯
a_0, a_1, a_2, \cdots
a
0
,
a
1
,
a
2
,
⋯
of nonzero real numbers such that for
n
=
1
,
2
,
3
,
⋯
n = 1, 2, 3, \cdots
n
=
1
,
2
,
3
,
⋯
the polynomial
p
n
(
x
)
=
a
0
+
a
1
x
+
a
2
x
2
+
⋯
+
a
n
x
n
p_n(x) = a_0 + a_1 x + a_2 x^2 + \cdots + a_n x^n
p
n
(
x
)
=
a
0
+
a
1
x
+
a
2
x
2
+
⋯
+
a
n
x
n
has exactly
n
n
n
distinct real roots?
algebra
polynomial
Putnam
college contests