Calculate the following by hand 397 eulers criterionSolution

Calculate the following by hand (3/97) eulers criterion

Since 97 is odd prime so by Euler\'s Criterion

(3/97)=3^{(97-1)/2}=3^{48} modulo 97

3^4=81=-16 modulo 97

3^8=(3^4)^2=(-16)^2=96=-1 modulo 97

3^{16}=(3^8)^2=1 modulo 97

3^{48}=(3^{16}^3=1 modulo 97

Hence,

(3/97)=1

$Calculate the following by hand (3/97) eulers criterionSolutionSince 97 is odd prime so by Euler\'s Criterion (3/97)=3^{(97-1)/2}=3^{48} modulo 97 3^4=81=-16 mo$

Calculate the following by hand 397 eulers criterionSolution

Solution

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