Integerksuch

Integerksuch is a term encountered in speculative mathematics and computer science to describe a family of concepts centered on searching for and characterizing integers that satisfy a user-defined predicate. It is not a standard term in established mathematical literature, and its exact meaning varies by author or context.

Definition and scope. Given a predicate P that assigns a true/false value to integers, an integer n is said to be an integerksuch with respect to P if P(n) holds. The idea also encompasses algorithmic tasks that, provided with P and a bound N, aim to enumerate all integers n with n ≤ N for which P(n) is true. Variants may specify additional constraints, such as limiting the search by magnitude, structure, or representation of n.

Examples of predicates. P(n) could be simple or complex: n is prime; the sum of digits of n is even; n can be expressed as a sum of two squares; n has a bounded number of nonzero digits in a given base; or n satisfies a modular condition. Each predicate defines a distinct class of integerksuch values.

Computation and methods. Finding integerksuch values typically relies on standard algorithmic techniques for the chosen predicate, such as primality tests, sieve methods, modular arithmetic, or constructive representations. The computational complexity depends on the predicate and the imposed bounds, and practical approaches often balance completeness with efficiency.

Usage and reception. As a flexible concept, integerksuch serves as a teaching and exploratory tool for predicate-based search in integers, illustrating how different properties shape enumeration problems and algorithm design. See also: search problems, decision problems, predicate logic.