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UltrafastPED

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Second, these are easier to understand than many more recent results, and are useful when you are learning how to attack these problems. For homework-type 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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Constructive Proofs
(open) Little Fermat Proof

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