Fermat's Theorem

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Fermat's theorem

[′fer‚mäz ‚thir·əm]
(mathematics)
The proposition that, if p is a prime number and a is a positive integer which is not divisible by p, then a p-1-1 is divisible by p.

Fermat’s Theorem

 

(or Fermat’s lesser theorem), a fundamental theorem of number theory. The theorem states that if p is a prime number and a is a whole number not divisible by p, then ap–1 – 1 is divisible by p—that is, ap–1 ≡ 1 (mod p). The theorem was set forth by P. Fermat without proof; the first proof was given by L. Euler.

References in periodicals archive ?
The following results are versions of Fermat Theorem and Rolle Theorem, respectively, in nonsmooth framework.