Determine the values of

47/37 and

3/43

stating any properties of the legendre symbol used.

is there just one method to solve all of these or are there different methods to solve depending on the numbers.

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- May 6th 2008, 02:18 PMRakeshLegendre symbol
Determine the values of

47/37 and

3/43

stating any properties of the legendre symbol used.

is there just one method to solve all of these or are there different methods to solve depending on the numbers. - May 6th 2008, 06:19 PMThePerfectHacker
$\displaystyle (47/37) = (10/37)$ ---> Congruence

$\displaystyle =(2/37)(5/37)$ ---> Multiplicative

$\displaystyle (2/37) = -1$ because $\displaystyle 37\equiv \pm 3(\bmod 8)$.

$\displaystyle (5/37) = (37/5)$ ---> Quadradic Reciprocity

$\displaystyle (37/5) = (2/5)$ ---> Congruence

$\displaystyle (2/5) = 1$ because $\displaystyle 5\equiv \pm 1(\bmod 8)$.

Thus, $\displaystyle (10/37) = (2/37)(5/37) = (-1)(1)=-1$. - May 6th 2008, 09:30 PMIsomorphism
- May 6th 2008, 11:30 PMjtsab
- May 7th 2008, 08:36 AMThePerfectHacker