The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…

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)

All the familiar numbers (rationals, algebraic numbers and a few transcendental numbers) have measure zero. (MM)

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 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…

A brief survey of the elementary number systems is provided. The natural numbers, integers, rational numbers, real numbers, and complex numbers are discussed; numerals and the use of numbers in measuring are also covered. (DT)

It is shown that a unit segment can be constructed from a given line segment of length the square root of x if x is a surd. (MP)

The question of whether the complex numbers can be ordered was investigated. (DT)