\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2010b.00335}
\itemau{McAndrew, Alasdair}
\itemti{Mathematical induction, difference equations and divisibility.}
\itemso{Int. J. Math. Educ. Sci. Technol. 40, No. 8, 1013-1025 (2009).}
\itemab
Summary: Many exercises in mathematical induction require the student to prove a divisibility property of a function of the integers. Such problems are generally presented as being independent of each other. However, many of these problems can be presented in terms of difference equations, and the theory of difference equations can be used to provide a uniform method for creating such divisibility problems. This article shows how a multitude of such problems can be created, and how standard problems from textbooks can be analysed in terms of difference equations.
\itemrv{~}
\itemcc{E50 F60}
\itemut{induction problems; divisibility; difference equations; number theory}
\itemli{doi:10.1080/00207390903121743}
\end