Modular Arithmetic (residue arithmetic) Definition/Meaning:  

Arithmetic based on the concept of the congruence relation defined on the integers and used in computing to circumvent the problem of performing arithmetic on very large numbers.
Let m₁, rn₂, ..., m_k be integers, no two of which have a common factor greater than one. Given a large positive integer n it is possible to compute the remainders or residues r₁,. r₂, . . . , r_k such that

n ≡ r₁ (mod m₁)
n ≡ r₂ (mod m₂)

        ........

n ≡  r_k (mod m_k)

Provided n is less than

m₁ x m₂ x ... x m_k

n can be represented by

(r₁,r_2,.........r_k)

This can be regarded as an internal representation of n. Addition, subtraction, and multiplication of two large numbers then involves the addition, subtraction, and multiplication of corresponding pairs, e.g.

(r₁,_,.......r_k) + (s₁,_,.......s_k) = (r₁+ s₁, ... , r_k + s_k)

Determining the sign of an integer or comparing relative magnitudes are less straightforward.

Near by Terms: Mode Modem Modifier Bits Modula Modular Arithmetic (residue arithmetic) Modular Programming Modulation Modulator Module Specification Module Testing (unit testing) MOHLL Monic Polynomial Monitor Monoid Monomorphism Monostable (one-shot) Monte Carlo Method MOSFET (MOS transistor) MOS Transistor Most Significant Character Mother Mother Board Motorola Mouse