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JacobiSymbol

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:
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Plot the sequence wrt the last argument:
In[1]:=
Click for copyable input
Out[1]=
Evaluate for large arguments:
Second argument may be even:
TraditionalForm formatting:
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:
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