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# pset2 - MIT OpenCourseWare http:/ocw.mit.edu 6.00...

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MIT OpenCourseWare http://ocw.mit.edu 6.00 Introduction to Computer Science and Programming Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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6.00: Introduction to Computer Science and Programming Problem Set 2 Introduction This problem set will introduce you to using control structures in Python and using exhaustive search as a problem solving technique. Collaboration You may work with other students. However, each student should write up and hand in his or her assignment separately. Be sure to indicate with whom you have worked. For further detail, please review the collaboration policy as stated in the syllabus. McDiophantine: Selling McNuggets In mathematics, a Diophantine equation (named for Diophantus of Alexandria, a third century Greek mathematician) is a polynomial equation where the variables can only take on integer values. Although you may not realize it, you have seen Diophantine equations before: one of the most famous Diophantine equations is: x n + y n = z n . For n=2, there are infinitely many solutions (values for x, y and z) called the Pythagorean triples, e.g. 3 2 + 4 2 = 5 2 . For larger values of n, Fermat’s famous “last theorem” states that there do not exist any positive integer solutions for x, y and z that satisfy this equation. For centuries, mathematicians have studied different Diophantine equations; besides Fermat’s last theorem, some famous ones include Pell’s equation, and the Erdos-Strauss conjecture. For more information on this intriguing branch of mathematics, you may find the
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## pset2 - MIT OpenCourseWare http:/ocw.mit.edu 6.00...

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