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

@article{Dries2003GeneratingTG,
  title={Generating the Greatest Common Divisor, and 
 Limitations of Primitive Recursive Algorithms},
  author={L. van den Dries},
  journal={Foundations of Computational Mathematics},
  year={2003},
  volume={3},
  pages={297-324}
}
AbstractThe 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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