The sum of the divisors of a positive integer is one of the most interesting concepts in multiplicative number theory, while the number of ways of expressing a number as a sum is a primary topic in additive number theory. In this article, we describe some of the surprising connections between and similarities of these two concepts.

This article describes the use of Fermi questions as a problem-solving tool.

As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…

An elementary arithmetic workbook in whole numbers for speakers of Hmong has an introductory section and a variety of exercises in conceptualizing, writing, spelling, and sequencing numbers from 0 to 999. (MSE)

The history of the two numbers e and pi is traced, and the relationship of thesetwo numbers to the history and development of mathematics is indicated. (DT)

This programed mathematics textbook is for student use in vocational education courses. It was developed as part of a programed series covering 21 mathematical competencies which were identified by university researchers through task analysis of several occupational clusters. The development of a sequential content structure was also based on…

This study traces the development of nondecimal numeration from the 16th century to the present. The first six chapters detail the contributions of mathematicians as well as people from other fields. Applications to computers are covered in one chapter, while another chapter discusses the coverage of numeration systems in college textbooks for…

This article presents some alternative formulae for Chinese-Western conversion of dates. (CHK)

Understanding rational numbers is often an elusive goal in mathematics. Presented is an approach for teaching rational numbers that has been used with many preservice and elementary school teachers. With some adaptation, the approach could be used with secondary school students. (RH)

This paper describes a design research study with ten second-grade students who are part of the Measure Up (MU) research and development project underway at the University of Hawai'i. Students were asked how they counted in multiple bases, specifically how they knew when to go to a new place value and why it was necessary to do so. All ten…

Theorems concerning the probability of the appearance of certain digits in a numeral are stated and proved. (DT)