Question

quadratic reciprocity law \[(m/n)(n/m) = (-1)^{\frac{m-1}{2} \frac{n-1}{2}}\]

\(m\ne n\) are odd primes

Answer 1

So far I have below :
\[\frac{(m-1)(n-1)}{4} = \sum\limits_{i=1}^{(m-1)/2}\left\lfloor \frac{in}{m}\right\rfloor + \sum\limits_{j=1}^{(n-1)/2}\left\lfloor \frac{jm}{n}\right\rfloor\]

Answer 2

@Marki

Answer 3

Just use gauss lemma (a/p)=(_1)powe the sum stuff

Answer 4

how ? let me look up gauss lemma quick..

Answer 5

Oh gauss lemma or theorem is very important result

Answer 6

Oh gauss lemma or theorem is very important result