chapter 4 definitions

Question 1

quadratic residue modulo p

Answer 1

Let p be a prime and a ∈ ℤ with a ̸≡ 0 mod p. Then a is a quadratic residue modulo p if there exists x ∈ ℤ such that x²≡amodp

Question 2

quadratic non-residue modulo p

Answer 2

if there are no such x s.t. x²≡amodp

Question 3

Legendre symbol (a / p)

Answer 3

Let p be a prime and a ∈ ℤ. The Legendre Symbol (a / p) is defined by
(a/p) = { 1 if a is a quadratic residue modulo p, -1 if a is a quadratic non-residue modulo p, 0 if a ≡ 0 modp

Question 4

least residue

Answer 4

Let p be an odd prime and a ∈ ℤ. The least residue modulo p of a is the unique integer b such that

(i) -1/2(p-1) ≤ b ≤ 1/2(p-1)
(ii) b≡amodp

Question 5

lattice point

Answer 5

and element of ℝ² that has integer co-ordinates