Exploring Topics in Elementary Number Theory Through A Computational Experiment
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Chapter 8 considers topics in the elementary theory of numbers that span from the time of Pythagoras to the time of Euler and connects ancient ideas about the properties of numbers that concerned Pythagoras and Euclid with more sophisticated interpretation of those ideas by Fermat and Euler. Whereas mathematical explorations that can be included in a computational experiment can be quite significant, software tools allow for hiding some of the complexity and formal structure of mathematics involved. This feature of computing is especially important for mathematics teacher education programs for it enables teacher candidates true engagement in dealing with rather advanced content without the need to have full understanding of the content and command of rigorous argument expected from future professional mathematicians.