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I guess the main real life application is to public key cryptography. It might be hard to come up with realistic examples at a sufficiently elementary level, but perhaps it would be possible to go some way in that direction.Are there any real life applications of linear Diophantine equations? I am looking for examples which will motivate students.
Hey eddybob.Other than that, I don't think number theory has any practical uses in real life. (Except maybe calculating restaurant bills, HST, etc.)
The main mathematical use of number theory is to "pave a road" into more advanced studies such as differential equations and abstract algebra, which themselves have countless applications in many scientific disciplines.
I do hope that Your students will be 'motivated' by the following 'brillant' application od diophantine equations that is datec from the Middle Ages. A well known fundamental theorem of the number theory is called 'Chinese Remainder Theorem' and it extablishes that if $n_{1}$ and $n_{2}$ are coprime, then the diophantine equation...Are there any real life applications of linear Diophantine equations? I am looking for examples which will motivate students.
Of course there are. For example, in molecular physics and organic chemistry.eddybob123 said:I don't think number theory has any practical uses in real life.