Jacobi Symbol

The product of Legendre Symbols for each of the Prime factors such that, denoted . When is a Prime, the Jacobi symbol reduces to the Legendre Symbol. TheJacobi symbol satisfies the same rules as the Legendre Symbol

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Bach and Shallit (1996) show how to compute the Jacobi symbol in terms of the Simple Continued Fraction of aRational Number .

References

Bach, E. and Shallit, J. Algorithmic Number Theory, Vol. 1: Efficient Algorithms. Cambridge, MA: MIT Press, pp. 343-344, 1996.

Guy, R. K. ``Quadratic Residues. Schur's Conjecture.'' §F5 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 244-245, 1994.

Riesel, H. ``Jacobi's Symbol.'' Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, pp. 281-284, 1994.

• Real Number
• Real Part
• Real Polynomial
• Real Projective Plane
• Real Quadratic Field
• Rearrangement Theorem
• Reciprocal
• Reciprocal Difference
• Reciprocal Polyhedron
• Reciprocating Sphere
• Reciprocation
• Reciprocity Theorem
• Rectangle
• Rectangle Function
• Rectangle Squaring
• Rectangular Coordinates
• Rectangular Distribution
• Rectangular Hyperbola
• Rectangular Parallelepiped
• Rectangular Projection
• Rectifiable Current
• Rectifiable Set
• Rectification
• Rectifying Latitude
• Rectifying Plane