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Turkey Team Selection Test
1996 Turkey Team Selection Test
1
Turkey TST 1996 Problem 1, find a_1996
Turkey TST 1996 Problem 1, find a_1996
Source: Turkey TST 1996 Problem 1
September 28, 2011
algebra proposed
algebra
Problem Statement
Let
∏
n
=
1
1996
(
1
+
n
x
3
n
)
=
1
+
a
1
x
k
1
+
a
2
x
k
2
+
.
.
.
+
a
m
x
k
m
\prod_{n=1}^{1996}{(1+nx^{3^n})}= 1+ a_{1}x^{k_{1}}+ a_{2}x^{k_{2}}+...+ a_{m}x^{k_{m}}
∏
n
=
1
1996
(
1
+
n
x
3
n
)
=
1
+
a
1
x
k
1
+
a
2
x
k
2
+
...
+
a
m
x
k
m
where
a
1
,
a
1
,
.
.
.
,
a
m
a_{1}, a_{1}, . . . , a_{m}
a
1
,
a
1
,
...
,
a
m
are nonzero and
k
1
<
k
2
<
.
.
.
<
k
m
k_{1} < k_{2} <...< k_{m}
k
1
<
k
2
<
...
<
k
m
. Find
a
1996
a_{1996}
a
1996
.
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