This article presents a method of reducing fractions without factoring. The ideas presented may be useful as a project for motivated students in an undergraduate number theory course. The discussion is related to the Euclidean Algorithm and its variations may lead to projects or early examples involving efficiency of an algorithm.

This paper takes a known point from Brocard geometry, a known result from the geometry of the equilateral triangle, and bring in Euler's [empty set] function. It then demonstrates how to obtain new Brocard Geometric number theory results from them. Furthermore, this paper aims to determine a [triangle]ABC whose Crelle-Brocard Point [omega]…

A study of a class of numbers called 'Good numbers' can provide students with many opportunities for investigation, conjecture, and proof. Definitions and proofs are presented along with suggested questions. (MNS)

The historical origin of star-polygons is noted and the mathematics of them presented, with illustrations. Seven theorems are included, as well as a computer program designed to classify star-polygons. (MNS)

Questions students raise about the meaning of zero to the zero power present an opportunity for mathematics teachers to involve students in active participation in exploring mathematical relationships. Calculators are the needed tool to make this exploration accessible to students. How they can be used is described. (MNS)

Representation of integers in various bases is explored, with a proof. (MNS)

A student noticed an interesting fact about the base two numerals for perfect numbers. Mathematical explanations for some questions are given. (MNS)