Question #161586

Evaluate kronecker symbol (11/24)


1
Expert's answer
2021-02-24T06:32:46-0500

If n=p1...pk,n=p_1...p_k, then (dn)=(dp1)...(dp2)(\dfrac{d}{n})=(\dfrac{d}{p_1})...(\dfrac{d}{p_2})


24=222324=2\cdot2\cdot2\cdot3

113(mod 8)11\equiv3(mod\ 8) Then (112)=1(\dfrac{11}{2})=-1

d(113)d(\dfrac{11}{3}) is the Legendre symbol: d(113)=1d(\dfrac{11}{3})=-1


d(1124)=d(112)d(112)d(112)d(113)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=-1(-1)(-1)(-1)=1

d(1124)=1d(\dfrac{11}{24})=1


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