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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Quadratic Residues

**Physics Forums | Science Articles, Homework Help, Discussion**