Answer to Question #161586 in Combinatorics | Number Theory for Geek

Question

Evaluate kronecker symbol (11/24)

Answer 1

If $n=p_1...p_k,$ then $(\dfrac{d}{n})=(\dfrac{d}{p_1})...(\dfrac{d}{p_2})$

$24=2\cdot2\cdot2\cdot3$

$11\equiv3(mod\ 8)$ Then $(\dfrac{11}{2})=-1$

$d(\dfrac{11}{3})$ is the Legendre symbol: $d(\dfrac{11}{3})=-1$

$$d(\dfrac{11}{24})=d(\dfrac{11}{2})d(\dfrac{11}{2})d(\dfrac{11}{2})d(\dfrac{11}{3})$$

$$=-1(-1)(-1)(-1)=1$$

$$d(\dfrac{11}{24})=1$$