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Problems
Contests
National and Regional Contests
Russia Contests
Soros Olympiad in Mathematics
VII Soros Olympiad 2000 - 01
8.7
8.7
Part of
VII Soros Olympiad 2000 - 01
Problems
(1)
(x+100) (x+99) ... (x-99)(x-100)=x^{201}+... (VII Soros Olympiad 2000-01 R1 8.7)
Source:
7/27/2021
In the expression
(
x
+
100
)
(
x
+
99
)
.
.
.
(
x
−
99
)
(
x
−
100
)
(x + 100) (x + 99) ... (x-99) (x-100)
(
x
+
100
)
(
x
+
99
)
...
(
x
−
99
)
(
x
−
100
)
, the brackets were expanded and similar terms were given. The expression
x
201
+
.
.
.
+
a
x
2
+
b
x
+
c
x^{201} + ...+ ax^2 + bx + c
x
201
+
...
+
a
x
2
+
b
x
+
c
turned out. Find the numbers
a
a
a
and
c
c
c
.
algebra
polynomial