This paper describes a study for teaching number system in a computer arithmetic course and addresses the existing gap in the current course by focusing on the characteristics of applications. A redundant residue number system (RRNS) is an efficient and innovative number system that inherits the interesting properties of both residue number system…

The aim of this study was to investigate second-grade elementary school students' performance related to their counting skills, place value understanding, and addition operation in natural numbers. A total of 205 second-grade elementary school students from Turkey participated in this study. The data were collected through a 'Personal Information…

The fundamental theorem of arithmetic is one of those topics in mathematics that somehow "falls through the cracks" in a student's education. When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like "every natural number can be broken down into a…

Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the…

This paper analyses the strategies used by pre-service primary school teachers for solving simple addition problems involving negative numbers. The findings reveal six different strategies that depend on the difficulty of the problem and, in particular, on the unknown quantity. We note that students use negative numbers in those problems they find…

This note can be used to illustrate to the student such concepts as periodicity in the complex plane. The basic construction makes use of the Tent function which requires only that the student have some working knowledge of binary arithmetic.

This short note demonstrates that even for smaller natural numbers, one can have some rule to follow when it comes to studying the divisibility by 4 and 8. One need not actually divide the number.

This article provides a survey of some basic results in algebraic number theory and applies this material to prove that the cyclotomic integers generated by a seventh root of unity are a unique factorization domain. Part of the proof uses the computer algebra system Maple to find and verify factorizations. The proofs use a combination of historic…

Some procedures are developed for testing divisibility by prime numbers composed of two or more digits. Accelerating the tests is also considered. (Contains 2 tables.)