In this module the problem of presenting an integer as a sum or as a difference of two squares is studied. Key questions considered are: which integers can be so represented? and what is the behavior of the average number of ways an integer can be represented? Students 1) practice and develop problem-solving skills; 2) become acquainted with the idea of congruence and its uses; 3) use the computer to gather facts about a problem; and 4) use geometry and calculus to help solve problems of representing integers.
Table of Contents:
1. INTRODUCTION
2. REPRESENTING AN INTEGER AS A DIFFERENCE OF SQUARES, I
3. CONGRUENCE AND RESIDUE ARITHMETIC
4. REPRESENTING AN INTEGER AS A DIFFERENCE OF SQUARES, II
5. THE AVERAGE NUMBER OF REPRESENTATIONS
6. REPRESENTING AN INTEGER AS A SUM OF TWO SQUARES (A SELF-TEST)
7. REFERENCES
8. ANSWERS TO EXERCISES
9. ANSWERS FOR SECTION 6 (THE SELF-TEST)
You must have a Full Membership to download this resource.
If you're already a member, login here.
COMAP develops curriculum resources, professional development programs, and contest opportunities that are multidisciplinary, academically rigorous, and fun for educators and students. COMAP's educational philosophy is centered around mathematical modeling: using mathematical tools to explore real-world problems.