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Lower-half quadratic-residue sum for primes congruent to seven modulo eight
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)
Mathematics
Area of mathematics
Number theory
Quadratic residue
Legendre symbol
Created
2026-09-24
Updated
2026-09-24
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If
p
≡
7
(
mod
8
)
, the
sum
of the least positive
quadratic residues
below
p
/2
is
16
p
2
−
1
.
(1)
The proof
uses
(
p
2
)
=
1
to compare the
sum
of all
residues
with its
image
under doubling.
Ancestors
(6)
Legendre symbol
Quadratic residue
Number theory
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2023
/
ii
/
Paper 4
/
11G
/
d
/
Solution
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