randommultiple

Randommultiple is a concept used in mathematics and computer science to describe a number chosen at random from the set of multiples of a given integer. Formally, let n be a nonzero integer. A random multiple X is defined as X = k n, where k is an integer random variable drawn from a specified distribution over integers.

In common practice, k is sampled uniformly from a finite interval [a, b], so that X takes values in {a n, (a+1) n, ..., b n}. Other integer distributions for k are possible, allowing X to have different probability properties. When the target range for X is not naturally aligned with n, techniques such as rejection sampling or transformation of the k-distribution may be used to achieve a desired level of uniformity or bias control.

Properties of a randommultiple depend on the distribution of k. If E[k] = mu and Var(k) = sigma^2, then E[X] = mu n and Var(X) = sigma^2 n^2. The choice of distribution for k determines the spread and bias of the resulting multiples.

Applications of randommultiples include randomized algorithms that operate on multiples of a base value, simulations involving modular arithmetic, and prototype explorations in number theory or cryptography where sampling from multiples is useful. Variants include random positive multiples, random nonzero multiples, or extensions to modular settings such as choosing random multiples within a residue class modulo m.

See also: uniform distribution, random number generation, multiples, modular arithmetic.