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Applications Diophantine Equations 
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#1
Aug1513, 11:12 AM

P: 153

Are there any real life applications of linear Diophantine equations? I am looking for examples which will motivate students.



#2
Aug1513, 12:16 PM

P: 772

All of the applications that I'm aware of are to other areas of mathematics. Are you teaching number theory? To be honest, if students in a course on number theory require "real world applications", they probably shouldn't be in a course on number theory.



#3
Aug1513, 05:18 PM

HW Helper
P: 2,264

^What do you have against applications?
I first became interested in Diophantine equations in high school when I was assigned two problems for homework. Some might object that they are not true applications. 1)You have forgotten how many eggs you have. You remember the following remainders (% means mod) x%2=1 x%3=1 x%4=1 x%5=1 x%6=1 x%7=0 What x are possible and what is the smallest possible x? Some methods of solution lead to a Diophantine equation such as 7a60b=1 2)In a sport game one can score a or b points (say 3 and 7) What scores are possible? What can you say about the possibilities for low vs high scores? Diophantine equations are used in chemistry (often not in a systematic way) to balance chemical equations Pell's equation gives rational approximations to square roots. Which you can contrast with the the Babylonians or Hero's method of divide and average. The arithmetic application that keeps on giving. The RSA algorithm. There are many math puzzles that use Diophantine equations. These may or may not interest students. How many ways can so and so... I'm thinking of a number so and so.. Bobs uncle is half as old as his cousin... this pirate gold question http://www.physicsforums.com/showthread.php?t=85009 If you have not already remind the students that many topics are closely related like Factorization algorithms Continued fractions Stern–Brocot tree Chinese remainder theorem Modular Multiplicative inverses Linear Diophantine equations Euclid's lemma Euclidean algorithm 


#4
Aug1613, 07:19 AM

P: 1,666

Applications Diophantine Equations
A number of years ago I posted somewhere on the internet that I do not recall, a treasure map to a priceless treasure but encrypted via RSA and included with it the decryption key. Maybe your students could find it and decode it. Expect a surprise. :) Edit: Ok, I found it. Jesus, didn't realize how good the search engines are. It's there if they look. 


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