Question

Which integers are quadratic residues of 11?s

Short answer

The quadratic residues of 11 are 1,3,4,5,9

Step-by-step solution

Step: 1

For,

$\begin{array}{r}x=0:x^{2}mod11=0^{2}mod11=0\\ x=1:x^{2}mod11=1^{2}mod11=1\\ x=2:x^{2}mod11=2^{2}mod11=4\\ x=3:x^{2}mod11=3^{2}mod11=9\\ x=4:x^{2}mod11=4^{2}mod11=5\\ x=5:x^{2}mod11=5^{2}mod11=3\\ x=6:x^{2}mod11=6^{2}mod11=3\\ x=7:x^{2}mod11=7^{2}mod11=5\\ x=8:x^{2}mod11=8^{2}mod11=9\\ x=9:x^{2}mod11=9^{2}mod11=4\\ x=10:x^{2}mod11={10}^{2}mod11=1\end{array}$

Step: 2

The quadratic residues of 11 are 1,3,4,5,9.