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.
ASJC Scopus subject areas
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics