numlib::isquadres -- test for
quadratic residues
IntroductionIf the integer number a is a quadratic residue modulo
the natural number m
numlib::isquadres(a,m) returns TRUE if the integer number
a is a quadratic residue modulo the natural number
m, and FALSE otherwise.
Call(s)numlib::isquadres(a, m)
Parametersa |
- | an integer |
m |
- | a natural number coprime to a |
Returnsnumlib::isquadres returns TRUE, FALSE, or the function call with its
arguments evaluated.
Related
Functionsnumlib::legendre,
numlib::jacobi,
numlib::msqrts
Detailsa is a quadratic residue modulo
the natural number m
numlib::isquadres(a,m) returns
TRUE, and if a is a quadratic non-residue
modulo m numlib::isquadres(a,m)
returns FALSE.a and m are not coprime
numlib::isquadres(a,m) returns an error.numlib::isquadres returns an error if the arguments
evaluate to numbers which are not both of the correct type.numlib::isquadres returns the function call with its
arguments evaluated if the arguments do not evaluate to numbers.
Example
1is a quadratic residue modulo :
>> numlib::isquadres(132132, 3231227)
TRUE
Example
2is a quadratic non-residue modulo :
>> numlib::isquadres(222222,324899)
FALSE
Example
3is a quadratic residue modulo :
>> numlib::isquadres(37,48884)
TRUE