Week 5

Question 1

define a quadratic residue modulo n and a quadratic non-residue modulo n

Question 2

prove that 1 has two square roots modulo 𝑝𝑒 where 𝑝 is an odd prime and 𝑒 is a positive integer

Question 3

determine the number of square roots of 1 modulo n for any positive integer n

Question 4

compute the square roots of 1 modulo n for a given value of n

Question 5

compute the square roots of a modulo n for any integer n and any integer a that is a quadratic residue modulo n

Question 6

determine the number of quadratic residues modulo n for any positive integer n

Question 7

define the Legendre symbol

Question 8

compute the Legendre symbol of a power of a primitive element

Question 9

use Euler’s Criterion to compute Legendre symbols

Question 10

use Gauss’ Lemma to compute Legendre symbols

Question 11

state the value of [legendre symbol with 2 over 𝑝] for any odd prime 𝑝