Q- A number is a quadratic residue modulo m if it takes the form x[tex]^{2}[/tex] mod m(adsbygoogle = window.adsbygoogle || []).push({});

for some integer x. List the quadratic residues modulo 3, 4, 5, and 7. What

patterns, if any, do you notice?

modulo 7

0^2=0, 1[tex]^{2}[/tex]=1, 2[tex]^{2}[/tex]=4, 3[tex]^{2}[/tex]=2, 4[tex]^{2}[/tex]=2, 5[tex]^{2}[/tex]=4, 6[tex]^{2}[/tex]=1

modulo 5

0^2=0, 1[tex]^{2}[/tex]=1, 2[tex]^{2}[/tex]=4, 3[tex]^{2}[/tex]=4, 4[tex]^{2}[/tex]=2

modulo 4

0^2=0, 1[tex]^{2}[/tex]=1, 2[tex]^{2}[/tex]=0, 3[tex]^{2}[/tex]=1

modulo 3

0^2=0, 1[tex]^{2}[/tex]=1, 2[tex]^{2}[/tex]=1

I don't to see any patterns?

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# Quadratic Residues

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