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1994 Tournament Of Towns
(411) 2
(411) 2
Part of
1994 Tournament Of Towns
Problems
(1)
TOT 411 1994 Spring O S2 a_{n+2}x^2 + a_{n+1}x+ a_n = 0
Source:
6/12/2024
The sequence of positive integers
a
1
a_1
a
1
,
a
2
a_2
a
2
,
.
.
.
...
...
is such that for each
n
=
1
n = 1
n
=
1
,
2
2
2
,
.
.
.
...
...
the quadratic equation
a
n
+
2
x
2
+
a
n
+
1
x
+
a
n
=
0
a_{n+2}x^2 + a_{n+1}x+ a_n = 0
a
n
+
2
x
2
+
a
n
+
1
x
+
a
n
=
0
has a real root. Can the sequence consist of (a)
10
10
10
terms, (b) an infinite number of terms?(A Shapovalov)
algebra
polynomial