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Fermat's Little Theorem 
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#1
Oct1613, 05:14 AM

P: 153

What use are Fermat’s Little Theorem and Wilson’s theorems in number theory? Do these theorems have any real life applications? We cannot use them to find primes as both are pretty inefficient for large numbers.



#2
Oct1613, 01:35 PM

Sci Advisor
Thanks
PF Gold
P: 1,911

First, they show that it is possible to answer some of these questions  this was historically important, as our knowledge is based upon the cumulative results of the past.
Second, these are easier to understand than many more recent results, and are useful when you are learning how to attack these problems. For homeworktype problems they work quite well. This is a partial answer to your first question ... as to useful applications today, it depends upon the application! If you always work with very large numbers, then they would not be the most efficient technique. But it depends upon your application. 


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