JacobiSymbol

gives the Jacobi symbol

Integer mathematical function, suitable for both symbolic and numerical manipulation.

For prime m, the Jacobi symbol reduces to the Legendre symbol. The Legendre symbol is equal to depending on whether n is a quadratic residue modulo m.

Compute Jacobi symbols:

Plot the sequence wrt the last argument:

Compute Jacobi symbols:

Out[1]=

Out[2]=

Plot the sequence wrt the last argument:

Out[1]=

Evaluate for large arguments:

Second argument may be even:

JacobiSymbol threads element-wise over lists and arrays:

JacobiSymbol works for negative first arguments:

Find Euler-Jacobi pseudoprimes:

The Gauss reciprocity law:

Construct eigenvectors of the discrete Fourier transform:

Evaluate Gauss sums in closed form:

Plot the nontrivial values of the Jacobi symbol:

Reduce equations containing JacobiSymbol:

Successive differences of JacobiSymbol modulo 2: