Question

Difference of quadratic residues and quatric residues

Answer 1

question:

Difference of quadratic residues and quatric residues

Answer:

QUADRATIC RESIDUES÷

In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n.

Otherwise, q is called a quadratic nonresidue modulo n.

Originally an abstract mathematical concept from the branch of number theory known as modular arithmetic, quadratic residues are now used in applications ranging from acoustical engineering to cryptography and the factoring of large numbers.

Quartic reciprocity÷

Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence x^4 ≡ p (mod q) to that of x^4 ≡ q (mod p).