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Generating the Greatest Common Divisor, and Limitations of Primitive Recursive Algorithms

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Abstract

The greatest common divisor of two integers cannot be generated in a uniformly bounded number of steps from those integers using arithmetic operations. The proof uses an elementary model-theoretic construction that enables us to focus on “integers with transcendental ratio.” This unboundedness result is part of the solution of a problem posed by Y. Moschovakis on limitations of primitive recursive algorithms for computing the greatest common divisor function.

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Correspondence to L. van den Dries.

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Communicated by Peter Olver

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van den Dries, L. Generating the Greatest Common Divisor, and Limitations of Primitive Recursive Algorithms. Found Comput Math 3, 297–324 (2003). https://doi.org/10.1007/s10208-002-0061-y

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  • DOI: https://doi.org/10.1007/s10208-002-0061-y

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