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.