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Arithmetic-term representations for the greatest common divisor

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arxiv 2411.06430 v2 pith:NQ3VF33I submitted 2024-11-10 math.NT math.LO

Mihai Prunescu , Joseph Shunia This is my paper · ORCID
classification math.NTmath.LO
keywords arithmetic-termrepresentationarithmeticbyproductcommonconstructdeducedivisor
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We construct a new arithmetic-term representation for the function gcd(a,b). As a byproduct, we also deduce a representation gcd(a,b) by a modular term in integer arithmetic.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On arithmetic terms expressing the prime-counting function and the n-th prime

    math.NT 2024-12 reject novelty 7.0 of 10

    The paper constructs, in principle, fixed-length arithmetic terms for the prime-counting function pi(n) and the n-th prime p(n), with p(n) expressed as a hypercube-derived count of solutions to a 42-variable exponenti...

  2. On non-holonomicity, transcendence and $p$-adic valuations

    math.NT 2024-12 conditional novelty 6.0 of 10

    Generating series of q-adic valuations are non-holonomic, non-algebraic over characteristic 0 fields, and take transcendental values at infinitely many rational and algebraic irrational points.

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