What is residue number?

Definition. A residue numeral system is defined by a set of k integers. called the moduli, which are generally supposed to be pairwise coprime (that is, any two of them have a greatest common divisor equal to one).

What is residue class in number theory?

Definition of residue class : the set of elements (such as integers) that leave the same remainder when divided by a given modulus.

What is residue arithmetic?

Carry independent arithmetic (called residue arithmetic) is possible within some limits. This residue arithmetic representation is a way of approaching a famous bound on the speed at which addition and multiplication can be performed.

What is another word for residue?

What is another word for residue?

remainder remnant
residuum surplus
dregs excess
lees remnants
grounds sediment

What is set residue?

(modulo n) A set of n integers, one from each of the n residue classes modulo n. Thus {0, 1, 2, 3} is a complete set of residues modulo 4; so too are {1, 2, 3, 4} and {−1, 0, 1, 2}. From: complete set of residues in The Concise Oxford Dictionary of Mathematics »

What is a residue group?

The residue classes prime to form a group under the binary multiplication operation (mod ), where. is the totient function (Shanks 1993) and the group is classed a modulo multiplication group.

What is meant by residue class 6?

residue: a small amount of something that remains after the main part has gone or been taken or used.

What is the residue of mod 9?

Law of quadratic reciprocity

a a is a quadratic residue mod p if and only if
8 p ≡ 1, 7 (mod 8)
9 (every prime p)
10 p ≡ 1, 3, 9, 13, 27, 31, 37, 39 (mod 40)
11 p ≡ 1, 5, 7, 9, 19, 25, 35, 37, 39, 43 (mod 44)

How do you solve quadratic residues?

We only need to solve, when a number (b) has a square root modulo p, to solve quadratic equations modulo p. Given a number a, s.t., gcd(a, p) = 1; a is called a quadratic residue if x2 = a mod p has a solution otherwise it is called a quadratic non-residue.

Is 0 a quadratic residue?

Modulo 2, every integer is a quadratic residue. Modulo an odd prime number p there are (p + 1)/2 residues (including 0) and (p − 1)/2 nonresidues, by Euler’s criterion. In this case, it is customary to consider 0 as a special case and work within the multiplicative group of nonzero elements of the field Z/pZ.

What is the opposite of residue?

▲ Opposite of refuse or waste material. treasure. valuables.