The problem of getting a correct result when a fraction is reduced by cancelling a digit which appears in both the numerator and the denominator is extended from the base ten situation to any number base. (DT)

This investigation concerns the repeated application of the rule "take the sum of the squares of the digits." (MP)

A test for divisibility by any prime number is discussed and its proof is given. (MP)

Two algorithms are developed for finding the square roots of numbers. One is based on the rule that x square is the sum of the first x odd numbers; the other is algebraic. (MP)

The method described here converts a given problem in a base other than ten to a related problem in base ten, solves the related problem in base ten, and converts the answer back to the original base. Limitations are discussed. (MP)

Algorithms are developed and presented for the addition and multiplication of positive rational numbers using only their repeating decimal representation. (MN)

A rationale is given for the Russian-peasant algorithm for multiplication indicating why it works as well as how it works. (DT)

After briefly presenting possible origins for the use of the decimal system for counting and the duodecimal (base twelve) system for many measures, a notational scheme using six positive'' digits and six negative'' digits is presented. Examples and algorithms using this set of digits for operations with whole numbers, fractions, and in…

The concept of prime factorization is discussed and two rules are developed: one for finding the number of divisors of a number and the other for finding the sum of the divisors. (MP)

In a thesis written for the Doctor of Arts in Mathematics, the connection between Euclid's algorithm and continued fractions is developed and extended to n dimensions. Applications to computer sciences are noted. (SD)