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A curious proof of fermat’s little theorem (801).
| Content Provider | CiteSeerX |
|---|---|
| Author | Alkauskas, Giedrius |
| Abstract | Fermat’s little theorem states that for p prime and a ∈ Z, p divides ap − a. This result is of huge importance in elementary and algebraic number theory. For instance, with its help we obtain the so-called Frobenius automorphism of a finite field Fpn over Fp. This theorem has many interesting and sometimes unexpected proofs. One classical proof is based upon properties of binomial coefficients. In fact, (d + 1) p −dp −1 = ∑p−1 p i p p! i=1 i d. Since i i!(p−i)! is divisible by p for 1 ≤ i ≤ p −1, then (d + 1) p − d p − 1 is divisible by p. Summing this over d = 1, 2,..., a − 1, we obtain the desired result. Another classical proof is based upon Lagrange’s |
| File Format | |
| Access Restriction | Open |
| Subject Keyword | Little Theorem Curious Proof Classical Proof Huge Importance Finite Field Fpn Unexpected Proof Desired Result Little Theorem State Binomial Coefficient So-called Frobenius Automorphism Algebraic Number Theory |
| Content Type | Text |
