Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

i know that $\left(\frac{1}{2}\right)=1$ since $1^2\equiv 1 \pmod2$ now since $3\equiv 1\pmod2$ we should have $\left(\frac{3}{2}\right)=\left(\frac{1}{2}\right)=1$ but on Maple i get that $\left(\frac{3}{2}\right)=-1$ why?

share|improve this question
    
The command \pmod produces the appropriate spacing and font for this. –  joriki Mar 2 '12 at 9:17

1 Answer 1

up vote 3 down vote accepted

The Legendre symbol, the Jacobi symbol and the Kronecker symbol are successive generalizations that all share the same notation. The first two are usually only defined for odd lower arguments (primes in the first case), whereas the Kronecker symbol is also defined for even lower arguments.

Since the distinction is merely historic, I guess it makes sense for math software to treat them all the same; Wolfram|Alpha returns $-1$ for JacobiSymbol(3,2). See the Wikipedia article for the definition for even lower arguments; the interpretation that a value of $-1$ indicates a quadratic non-residue is no longer valid in this case.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.