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1700
Cyclotomic Remainder
Editorial
algebra
polynomials
roots of unity
cyclotomic polynomials
Let
f
(
x
)
=
x
66
+
x
65
+
⋯
+
x
+
1
f(x) = x^{66} + x^{65} + \cdots + x + 1
f
(
x
)
=
x
66
+
x
65
+
⋯
+
x
+
1
. Find the remainder when
f
(
x
67
)
f(x^{67})
f
(
x
67
)
is divided by
f
(
x
)
f(x)
f
(
x
)
.
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