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Moscow Mathematical Olympiad
1951 Moscow Mathematical Olympiad
202
MMO 202 Moscow MO 1951 (x^{1951}-1):(x^4+x^3+2x^2+x+1)
MMO 202 Moscow MO 1951 (x^{1951}-1):(x^4+x^3+2x^2+x+1)
Source:
August 7, 2019
polynomial
coefficient
algebra
Problem Statement
Dividing
x
1951
ā
1
x^{1951} - 1
x
1951
ā
1
by
P
(
x
)
=
x
4
+
x
3
+
2
x
2
+
x
+
1
P(x) = x^4 + x^3 + 2x^2 + x + 1
P
(
x
)
=
x
4
+
x
3
+
2
x
2
+
x
+
1
one gets a quotient and a remainder. Find the coefficient of
x
14
x^{14}
x
14
in the quotient.
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