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numtheory

  

quadres

  

check if a number is a quadratic residue mod another

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

quadres(a, b)

Parameters

a, b

-

integer

Description

• 

Important: The numtheory[quadres] command has been deprecated.  Use the superseding command NumberTheory[QuadraticResidue] instead.

• 

The function quadres will compute a generalized Legendre symbol Lab of a and b, which is defined to be 1 if a is a quadratic residue modband -1 if a is a quadratic non-residue modp.  The number a is a quadratic residue mod b if it has a square root modb;  i.e., an integer c exists such that c2 is congruent to amodb.

• 

The command with(numtheory,quadres) allows the use of the abbreviated form of this command.

Examples

withnumtheory:

quadres74,101

1

(1)

quadres0,73

1

(2)

quadres22,11

1

(3)

quadres5,256

1

(4)

quadres2342,1904

1

(5)

See Also

numtheory[jacobi]

numtheory[legendre]