divideswhether

Divideswhether is a neologism used in informal discussions to denote a boolean predicate that expresses the question “does a divide b?” It is not part of standard mathematical terminology, but has appeared in puzzle forums and programming-language discussions to emphasize the decision aspect of divisibility.

Definition and semantics: In formal terms, divideswhether(a, b) is true exactly when there exists an integer k such that b = a·k, equivalently when b mod a = 0. When a is zero, divisibility is typically undefined or treated with specific conventions, so most writers constrain a to be nonzero. The predicate is functionally equivalent to the usual divisibility relation a | b, but the name highlights the question form rather than the static relation.

Examples: divideswhether(12, 36) yields true; divideswhether(12, 35) yields false; divideswhether(7, 21) yields true; divideswhether(7, 22) yields false.

Usage and context: In programming and formal discussions, divideswhether can be implemented as a boolean function is_divisible(a, b) that returns (b mod a == 0) for a ≠ 0. It is sometimes used to distinguish the act of asking whether divisibility holds from asserting that it does, which can aid in problem statements, proofs, or algorithm design.

Notes: Because divideswhether is not widely standardized, precision is important when using the term. In formal mathematics, it is usually clearer to refer directly to the divisibility relation “a divides b” (a | b) rather than the more colloquial predicate divideswhether.