On Euclid’s algorithm and elementary number theory - Backhouse, Roland; Ferreira, João F. (Elsevier B.V., 2011)
Algorithms can be used to prove and to discover new theorems. This paper shows how algorithmic skills in general, and the notion of invariance in particular, can be used to derive many results from Euclid’s algorithm. We illustrate how to use the algorithm as a verification interface (i.e., how to verify theorems) and as a construction interface (i.e., how to investigate and derive new theorems).