## Automating elementary number-theoretic proofs using Gröbner bases

Citations: | 4 - 0 self |

### BibTeX

@MISC{Harrison_automatingelementary,

author = {John Harrison},

title = {Automating elementary number-theoretic proofs using Gröbner bases},

year = {}

}

### OpenURL

### Abstract

Abstract. We present a uniform algorithm for proving automatically a fairly wide class of elementary facts connected with integer divisibility. The assertions that can be handled are those with a limited quantifier structure involving addition, multiplication and certain number-theoretic predicates such as ‘divisible by’, ‘congruent ’ and ‘coprime’; one notable example in this class is the Chinese Remainder Theorem (for a specific number of moduli). The method is based on a reduction to ideal membership assertions that are then solved using Gröbner bases. As well as illustrating the usefulness of the procedure on examples, and considering some extensions, we prove a limited form of completeness for properties that hold in all rings. 1