Successive Differences and Accumulations of the Jacobi Symbol

index of Jacobi modulus

3

prime Legendre moduli

include even Jacobi moduli

prime inputs

successive

pairwise accumulations

differences

accumulation

identity

gray negative range

render modulus

2

Render modular results of successive accumulations or differences for Jacobi symbols for the range -59 to 59. The Jacobi symbol extends the Legendre symbol, allowing a generalization of Gauss's celebrated quadratic reciprocity theorem.

Details

A number

n

is called a quadratic residue modulo

m

if there is a positive integer

x

such that

2

x

≡n(modm)

. The Jacobi symbol

n

m

is 0 for numbers

n

and

m

with a common factor, 1 if

n

is a quadratic residue modulo

m

, and -1 otherwise. The Jacobi symbol reduces to the Legendre symbol if

m

is an odd prime

p

.

External Links

Jacobi Symbol (Wolfram MathWorld)

Legendre Symbol (Wolfram MathWorld)

Quadratic Reciprocity Theorem (Wolfram MathWorld)

Permanent Citation

Michael Schreiber

"Successive Differences and Accumulations of the Jacobi Symbol"
http://demonstrations.wolfram.com/SuccessiveDifferencesAndAccumulationsOfTheJacobiSymbol/
Wolfram Demonstrations Project
Published: September 28, 2007