## 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 |
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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 |
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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.