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Multiplicativity of the Jacobi symbol
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Mathematics
Area of mathematics
Number theory
Jacobi symbol
2026-09-29
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For odd positive
n
, the
Jacobi symbol
is multiplicative in its
numerator
:
(
n
ab
)
=
(
n
a
)
(
n
b
)
.
(1)
It is also multiplicative in an odd
denominator
:
(
a
/
mn
)
=
(
a
/
m
)
(
a
/
n
)
.
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(5)
Jacobi symbol
Number theory
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2020
/
ii
/
Paper 3
/
1H
/
Solution
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