DIVISIBILITY OF A NEAR-PRODUCT: AN EXERCISE IN PATTERN DISCOVERY AND PROOF BY INDUCTION.

The article presents a numerical pattern whose proof provides a perfect example of mathematical induction. It notes that numerous examples supporting a conjecture will not be able to constitute a proof. For equations with small number of variables, some students with a technology interest have found it appealing to locate solutions by an exhaustive search, with the assistance of computer programs or by using computer algebra system. According to the author, induction argument will not be easy for most undergraduate students but can provide a perfect exercise to help them better appreciate the power of the fundamental method of proof.