Solving Diophantine Equations Using Python

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Published on 2010-06-16T03:06:05Z Indexed on 2010/06/16 3:12 UTC
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diophantine

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:

We are not certain that McDonald's knows about Diophantine equations (actually we doubt that they do), but they use them! McDonald's sells Chicken McNuggets in packages of 6, 9 or 20 McNuggets. Thus, it is possible, for example, to buy exactly 15 McNuggets (with one package of 6 and a second package of 9), but it is not possible to buy exactly 16 nuggets, since no non- negative integer combination of 6's, 9's and 20's adds up to 16. To determine if it is possible to buy exactly n McNuggets, one has to solve a Diophantine equation: find non-negative integer values of a, b, and c, such that

        6a + 9b + 20c = n.

Write an iterative program that finds the largest number of McNuggets that cannot be bought in exact quantity. Your program should print the answer in the following format (where the correct number is provided in place of n):

"Largest number of McNuggets that cannot be bought in exact quantity: n"

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