# Minicourse for Undergraduates: Harshad Numbers and Sage Programming

## Modern Math Workshop 2015 October 28, 2015 - October 29, 2015

**Speaker(s):**Alejandra Alvarado (U.S. Navy), Helen Grundman (Bryn Mawr College), Pamela Harris (University of Wisconsin-Milwaukee)

**Primary Mathematics Subject Classification**No Primary AMS MSC

**Secondary Mathematics Subject Classification**No Secondary AMS MSC

A Harshad number is a positive integer that is divisible by the sum of its digits. The word “Harshad” comes from the Sanskrit harsa (joy) *+* da (give), meaning joy-giver, which was defined by the Indian mathematician D.R. Kaprekar. All one digit numbers are Harshad numbers and it is fairly simple to determine which two digit numbers are Harshad. In 1994, H. Grundman generalized the concept to *b*-Harshad (or *b*-Niven) numbers. Simply put, for b > 1, a *b*-Harshad number is a positive integer that is divisible by the sum of the digits of its base *b* expansion. The mini-course will provide undergraduate students with an opportunity to learn about Harshad numbers and how to compute some of their properties using the freely available mathematical program Sage. No prior programing experience is required.

Pre-requisite: An undergraduate algebra or number theory course