gcdabab

Gcdabab is a term that appears in online mathematics and puzzle communities as a playful designation for a family of operations related to the greatest common divisor (gcd). The name combines gcd with the idea of alternating or paired inputs, and there is no single canonical definition. In informal use, gcdabab serves as a container for different puzzles or constructions that reference gcd while introducing an alternating or iterative flavor.

Common variants

- Simple synonym: In many discussions gcdabab(a, b) is used simply as gcd(a, b). This keeps the term as a mnemonic for gcd without proposing a new operation.

- Alternating-iteration variant: Take a0 = a and a1 = b, and define an+2 = gcd(an, an+1) for n ≥ 0. The sequence tends to stabilize at a fixed value, which in standard integer arithmetic is the gcd(a, b). Thus gcdabab(a, b) equals gcd(a, b) in this interpretation, but the iterative rule is used for puzzle exploration of convergence properties.

- Sequence-pair variant: When a and b represent sequences or lists, gcdabab(A, B) might denote the gcd of a set of pairwise gcds {gcd(ai, bi)} or a related pairing construction. This version is common in problem statements designed to test understanding of gcd behavior on structured inputs.

Examples

- gcdabab(60, 28) with the simple variant yields 4, the gcd of 60 and 28.

- With the alternating-iteration variant, the sequence is 60, 28, gcd(60,28)=4, gcd(28,4)=4, …, stabilizing at 4.

Notes and usage

Gcdabab lacks formal status in mathematics and is primarily a convenience in problem-setting and discussion to draw attention to gcd-related ideas, especially involving alternating or iterative procedures. See also gcd, the Euclidean algorithm, and problems on convergence of gcd sequences.

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