6 - Fermat's Theorem and its Consequences

Table of contents

• 6.1 Fermat’s Theorem
• 6.2 Some Properties of Binomial Coefficients
• 6.3 A Second Proof of Theorem 72
• 6.4 Proof of Theorem 22
• 6.5 Quadratic Residues
• 6.6 Special Cases of Theorem 79: Wilson’s Theorem
• 6.7 Elementary Properties of Quadratic Residues and Non-Residues
• 6.8 The order of a \pmod m
• 6.9 The Converse of Fermat’s Theorem
• 6.10 Divisibility of 2^p - 1 by p^2
• 6.11 Gauss’s Lemma and the Quadratic Character of 2
• 6.12 The Law of Reciprocity
• 6.13 Proof of the Law of Reciprocity
• 6.14 Tests for Primality
• 6.15 Factors of Mersenne Numbers: a Theorem of Euler

6.1 Fermat’s Theorem

6.2 Some Properties of Binomial Coefficients

6.3 A Second Proof of Theorem 72

6.4 Proof of Theorem 22

6.5 Quadratic Residues

6.6 Special Cases of Theorem 79: Wilson’s Theorem

6.7 Elementary Properties of Quadratic Residues and Non-Residues

6.8 The order of a $(\mathrm{mod}m)$

6.9 The Converse of Fermat’s Theorem

6.10 Divisibility of $2^p-1$ by $p^2$

6.11 Gauss’s Lemma and the Quadratic Character of 2

6.12 The Law of Reciprocity

6.13 Proof of the Law of Reciprocity

6.14 Tests for Primality

6.15 Factors of Mersenne Numbers: a Theorem of Euler