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Proof and Refutations is a book by the philosopher Imre Lakatos expounding his view of

the progress of mathematics. The book is written as a series of Socratic dialogues involving a group of students. A central theme is that definitions are not carved in stone, but often have to be patched up in the light of later insights, in particular failed proofs. This gives mathematics a somewhat experimental flavour.

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Proofs of Fermat's little theoremThis is a collection of proofs of Fermat's little theorem: a p a ( mod p for every prime number p and every integer a''. Note that it is enough to prove a p − 1 1 (mod p for every integer a which is relatively prime to p (i. not a multiple of p .

Proofs and RefutationsProof and Refutations is a book by the philosopher Imre Lakatos expounding his view of the progress of mathematics. The book is written as a series of Socratic dialogues involving a group of students. A central theme is that definitions are not carved in

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